Short Programme on Probability and Statistical mechanics
Short Programme on Probability and Statistical mechanics
Content
Conference Agenda (updating)
Date: Oct. 9 to Nov. 10, 2017
Register date & place: Oct. 8, 2017 at New Office Builing, AMSS, CAS
Venue: N202, New Office Building, AMSS, CAS
C1 is the identifier of minicourse given by Professor Auffinger. See the others in the list of minicourses.
S1 is the identifier of seminar talk given by Professor Auffinger. See the others in the list of seminars.
Time  Oct. 9 (Mon)  Oct. 10 (Tues)  Oct. 11 (Wed)  Oct. 12 (Thur)  Oct. 13 (Fri)  Oct. 14 (Sat)  Oct. 15 (Sun)  
AM  09:3010:30 
C9 (I) Hao Wu 
C9 (II) Hao Wu 

C7 (I) 
C7 (II) Zhonggen Su 
C7 (III) Zhonggen Su 

10:3011:30  
Lunch  
PM  14:3015:30 
C2 (I) 
S3, Mufa Chen 
C2 (II) 
C6 (I) Vladas Sidoravicius 
S2, Gerard Ben Arous  
15:3016:30  S14, Vladas Sidoravicius  
16:3017:30  
Dinner  
19:0020:30 
Time  Oct. 16 (Mon)  Oct. 17 (Tues)  Oct. 18 (Wed)  Oct. 19 (Thur)  Oct. 20 (Fri)  Oct. 21 (Sat)  Oct. 22 (Sun)  
AM  09:3010:30 
C9 (III) Hao Wu 
C9 (IV) Hao Wu 
S5, Geoffrey Grimmett  S6, Geoffrey Grimmett  S8, Zechun Hu 

10:3011:30  S10, Takashi Kumagai  
Lunch  
PM  14:3015:30 
C3 (I) Andreas Kyprianou 
S7, Yaozhong Hu 
C3 (II) Andreas Kyprianou 
C6 (II) Vladas Sidoravicius 
C3 (III) Andreas Kyprianou 

15:3016:30  
16:3017:30  S9 (I), Daniel Kious  S9 (II), Daniel Kious  
Dinner  
19:0020:30 
Time  Oct. 23 (Mon)  Oct. 24 (Tues)  Oct. 25 (Wed)  Oct. 26 (Thur)  Oct. 27 (Fri)  Oct. 28 (Sat)  Oct. 29 (Sun)  
AM  09:3010:30 
C9 (V) Hao Wu 
C9 (VI) Hao Wu 
C4 (I) Leonardo Rolla 
S17, Jiangang Ying  
10:3011:30  
Lunch  
PM  14:3015:30 
S15, Jie Xiong 
S11, Zenghu Li 

C6 (III) Vladas Sidoravicius 
C4 (II) Leonardo Rolla 

15:3016:30  S16, Lihu Xu  
16:3017:30  S13, Alejandro Ramirez  
Dinner  
19:0020:30 
Time  Oct. 30 (Mon)  Oct. 31 (Tues)  Nov. 1 (Wed)  Nov. 2 (Thur)  Nov. 3 (Fri)  Nov. 4 (Sat)  Nov. 5 (Sun)  
AM  09:3010:30  C5 (I) QiMan Shao 
C5 (III) QiMan Shao 
Workshop Agenda  Young Forum Agenda 

10:3011:30  
Lunch  
PM  14:3015:30  S4, Shizan Fang  C5 (II) QiMan Shao 
S18, Xicheng Zhang  Workshop Agenda  Young Forum Agenda 

15:3016:30  
16:3017:30  
Dinner  
19:0020:30 
Time  Nov. 6 (Mon)  Nov. 7 (Tues)  Nov. 8 (Wed)  Nov. 9 (Thur)  Nov. 10 (Fri)  
AM  09:3010:30 
C1 (I) 
C1 (II) 
C1 (III) 
C8 (II) 

10:3011:30  
Lunch  
PM  14:3015:30 

S12, Kening Lu 
S1, Antonio Auffinger 
C8 (I) Pierre Michel Tarres 
C8 (III) Pierre Michel Tarres 
15:3016:30  
16:3017:30  
Dinner  
19:0020:30 
MiniCourses
C1  Firstpassage percolation: an introduction with many open problems 
Speaker  Professor Antonio Auffinger, Northwestern University (USA) 
Time  09:3011:30 Nov. 7, 8 and 9 (3 lectures) 
Place  N202 
Abstract  This course is an introduction to one of the most classical models in probability theory, the model of firstpassage percolation (FPP). During the lectures we will describe the main results of FPP, paying special attention to the recent burst of advances of the past 5 years. First, we will give selfcontained proofs of seminal results obtained in the ’80s and ’90s on limit shapes and geodesics, while covering the state of the art of these questions. Second, aside from these classical results, we discuss recent perspectives and directions including focusing on the connection between Busemann functions and geodesics. Many interesting open problems will be presented. 
C2  Interacting particle systems on trees 
Speaker  Professor Dayue Chen, Peking University 
Time  14:3016:30, Oct. 9 and 11 (2 lectures) 
Place  N202 
Abstract  We shall review several models of interacting particle systems on trees: contact process, exclusion process, Ising model, etc. We will investigate the relation between the underlying space structure and the limiting behaviors of an interacting particle system. In particular we like to find out the difference of a particle system on a lattice and on a tree. We will list some problems to be studied. 
C3  Exploration of $R^d$ by the isotropic alphastable process 
Speaker  Professor Andreas Kyprianou, Bath University 
Time  14:3016:30 Oct. 16, 18 and 20 (3 lectures) 
Place  N202 
Abstract  In this minicourse we will review some very recent work on isotropic stable processes in high dimension. The recent theory of selfsimilar Markov and Markov additive processes gives us new insights into their trajectories. Combining this with classical methods, we revisit some old results, as well as offering new ones. 
C4  Overview and Recent Progress in AbsorbingState Phase Transitions 
Speaker  Professor Leonardo Rolla, NYUShanghai 
Time  09:3011:30, 14:3016:30 Oct. 27 (2 lectures) 
Place  N202 
Abstract  *tentative only* Modern statistical mechanics offers a large class of drivendissipative stochastic systems that naturally evolve to a critical state, of which Activated Random Walks are perhaps the best example. The main pursuit in this field is to show universality of critical parameters, describe the critical behavior, the scaling relations and critical exponents of such systems, and the connection between drivendissipative dynamics and conservative dynamics in infinite space. This problem was stuck for more than a decade, then it saw significant partial progress about 9 years ago, and got stuck again. In this talk we will report on exciting progress made in the last 4 years, thanks to the contributions of Basu, Cabezas, Ganguly, Hoffman, Sidoravicius, Stauffer, Taggi, Teixeira, Tournier, Zindy, and myself. We will also discuss some of the several open problems. 
C5  Basic Probability Inequalities and Stein's Method 
Speaker  Professor QiMan Shao, Chinese University of Hong Kong 
Time  09:3011:30 Oct. 31 and Nov. 1, 14:3016:30 Oct. 31 (3 lectures) 
Place  N202 
Abstract  In this short course we shall review some basic probability inequalities and Stein's method. Probability inequalities have played an important role in various proofs. Stein's method is a completely different method from the classical Fourier method. It works for both independent and dependent random variables. It can also provide an accuracy of the approximation. The course will focus on the main idea of the method and recent development. 
C6  Percolation  old problems and new challanges 
Speaker  Professor Vladas Sidoravicius, NYUShanghai 
Time  14:3017:30 Oct. 12 and 26, 14:3016:30 Oct. 19 (3 lectures) 
Place  N202 
Abstract  During this course I will introduce Bernoulli percolation model and other models related to Statistical Physics, such as Ising and Random Cluster models, and establish some basic properties, such as existence of the phase transition; new proof by DuminilCopin and Tassion of the sharpness of the phase transition; the continuity of the phase transition in dimension two (Harris Theorem and Kesten Theorem). Next lectures will be devoted to renormalization techniques. In particular we will focus on BarskyGrimmettNewman method, and then discuss percolation on slabs, where we show its "well behavior" (Grimmett  Marstrand Theorem), and finally we will prove continuity of the phase transition on slabs. In the final lectures we will focus on the combinatorial/geometric methods to study phase transitions, in particular random currents representation and show continuity of the phase transition for the Ising model in any dimension. During this course I also will discuss many deep, mathematically challenging open problems. 
C7  Determinantal Point Processes with Applications 
Speaker  Professor Zhonggen Su, Zhejiang University 
Time  09:3011:30 Oct. 13, 14 and 15 (3 lectures) 
Place  N202 
Abstract  A determinantal point process is a random point process whose correlation functions can be expressed as a determinant of a kernel function. Determinantal point processes arise naturally in a number of apparently distinct probability models, and the focus is upon the study of kernel functions. In this short course, I shall first recall some basic concepts of point processes, correlations and provide some typical examples like Poisson processes, GUE and Noncolliding random processes. And then I will turn to asymptotic behaviours for a few of common probability models using determinantal point processes. It includes the law of large numbers, the central limit theorems for the number of particles inside an interval, and TracyWidom type laws for the rightmost particles. 
C8  Selfinteracting random walks and statistical physics  
Speaker  Professor Pierre Michel Tarres, NYUShanghai  
Time  14:3016:30 Nov. 9 and 10, 09:3011:30 Nov. 10 (3 lectures)  
Place  N202  
Abstract  We will review various techniques for the study of selfinteracting random walks, with a focus on the following topics: 1) Local time: introduced by RayKnight for the study of Markov chains, the technique was first used in that context by Tóth in the 90s in a series of papers analysing a large class of selfinteracting walks on the integer graph. In the nonexchangeable but selfrepelling case, Tarrès, Tóth and Valkó (resp. Horváth, Tóth and Vetö) were able to describe in 2012 that dynamics of the local time from the point of view of the particle for Brownian polymers (resp. selfavoiding walks), at the cost of losing information on the current position of the walk; see also Benaim, Ciotir and Gauthier (2015) in the compact case. 2) Coupling with Poisson Point Processes: initially proposed by Sellke (1994) for the study of strongly edgereinforced random walks, the coupling was adapted to the study of vertexreinforced random walk by Tarrès (2011), Basdevant, Schapira Singh (2014) (see also Kious (2016) for the socalled “stuck walks”) 3) Link with statistical physics, in particular the explicit correspondance between EdgeReinforced Random Walk (ERRW), the supersymmetric hyperbolic sigma model (Sabot and Tarrès 2015), the random Schrödinger operator (Sabot, Tarrès and Zeng 2016) and Dynkin's isomorhism (Sabot and Tarrès 2016). 
C9  Conformal invariance in critical 2D lattice models 
Speaker  Professor Hao Wu, Tsinghua University 
Time  09:3011:30 Oct. 9, 11, 16, 18, 23, 25 (6 lectures) 
Place  N202 
Abstract 
Conformal invariance and critical phenomena in 2D statistical physics have been active areas of research in the last few decades, both in the mathematics and physics communities. In 1999, Oded Schramm introduced Schramm Loewner Evolution which provides a novel way to understand twodimensional statistical lattice models. In this course, we will explain S. Smirnov’s work: the conformal invariance of the critical percolation and the conformal invariance of the critical Ising model. 
Seminars (updating)
S1  The SherringtonKirkpatrick model 
Speaker  Professor Antonio Auffinger, Northwestern University 
Time  14:3016:30 Nov. 8 
Place  N202 
Abstract  In this talk, I will survey the main results on the archetype model of spin glasses in the past 10 years, the SK model. I will start with Parisi's prediction, explain the Parisi formula as proved by Talagrand, the ultrametricity theorem of Panchenko and end with a proof of full replica symmetry breaking at zero temperature. Talk is also based on results with WeiKuo Chen and Qiang Zeng. 
S2  Complexity of random functions of many variables 
Speaker  Professor Gerard Ben Arous, Courant Institute 
Time  14:3015:30 Oct. 13 
Place  N202 
Abstract  Functions of many variables may be very complex. And optimizing them can be excedingly difficult or slow. Think for instance of the following simple question: How hard is it to find the minimum on the unit sphere of a cubic polynomial of many variables? If you chose the cubic polynomial randomly, it is very hard. Indeed it will have many local minima that will trap any algorithm trying to find the absolute minimum. First, I will adress the natural question: why does one care about this phenomenon? I will use examples in Data Science, and physics, where minimizing such functions is both important and hard. I will then explain briefly that one can describe and compute the complexity of functions of many variables, using the tools of Random Matrix Theory through a dictionary given by a classical formula of random geometry, the KacRice formula. 
S3  Mathematical Topics Motivated From Statistical Physics 
Speaker  Professor MuFa Chen, Beijing Normal University 
Time  14:3016:30, Oct. 10 
Place  N202 
Abstract  The talk consists of two parts: (1) From equilibrium to nonequilibrium. A typical class of nonequilibrium particle systems  reactiondiffusion processes; (2) The stability speed and the phase transitions. Spectral theory, the leading eigenvalue and so on. The first part is devoted to explore the mathematical foundation of statistical physics, the nonequilibrium systems in particular. The second part is to look for or to develop some mathematical tools for studying the phase transition phenomenon in statistical physics. The most part of the talk is informal. 
S4  Lagrange's description of mechanics of fluids 
Speaker  Professor Shizan Fang, University of Bourgogne 
Time  14:3016:30, Oct. 30 
Place  N202 
Abstract  A survey for introductions. 
S5  Counting selfavoiding walks 
Speaker  Professor Geoffrey Grimmett, Cambridge University 
Time  09:3010:30 Oct. 19 
Place  N202 
Abstract  The problem of selfavoiding walks (SAWs) arose in statistical mechanics in the 1940s, and has connections to probability, combinatorics, and the geometry of groups. The basic question is to count SAWs. The socalled 'connective constant' is the exponential growth rate of the number of nstep SAWs. We summarise joint work with Zhongyang Li concerned how the connective constant depends on the choice of graph. This work includes equalities and inequalities for connective constants, and a partial answer to the socalled ‘locality problem' for graphs and particularly Cayley graphs. 
S6  The 12 model: dimers, polygons, and the complex Ising model 
Speaker  Professor Geoffrey Grimmett, Cambridge University 
Time  09:3010:30 Oct. 20 
Place  N202 
Abstract  The 12 model is a disordered interacting system in two dimensions which can be mapped to a number of well known processes including the dimer, Ising, and polygon systems of probability theory and mathematical physics. These connections will be explained in this lecture, and the exact solution will be summarised (joint work with Zhongyang Li). 
S7  Some aspects of stochastic heat equations 
Speaker  Professor Yaozhong Hu, University of Alberta at Edmonton 
Time  14:3016:30 Oct. 17 
Place  N202 
Abstract  I will start with some basic concepts on stochastic heat equation.Then I will introduce and prove the FeynmanKac formulas for the solution and for the moments of the solution. These formulas will be applied to obtain the sharp upper and lower bounds for the moments of the solution. Most of the talk are for noise determined by general Gaussian process applicable to fractional Brownian field with Hurst parameter greater than 1/2. I will also mention some recent work on the case Hurst parameter H<1/2. 
S8  Hunt's Hypothesis (H) and Getoor's Conjecture 
Speaker  Professor Zechun Hu, Sichuan University 
Time  09:3011:30, Oct. 21 
Place  N202 
Abstract  This talk discusses Hunt's hypothesis (H) and Getoor's conjecture. It contains five parts. Firstly, I will talk about the background on Hunt's hypothesis (H). Secondly, I will recall the meaning of Hunt’s hypothesis (H) and its importance. Thirdly, I will introduce Getoor's conjecture and the existing results. Fourthly, I will introduce our results. Finally, I will mention some open problems. The talk is based on joints works with Wei Sun and Jing Zhang. 
S9  The Oncereinforced random walk 
Speaker  Professor Daniel Kious, NYU Shanghai 
Time  16:3017:30, Oct. 19 and 20 
Place  N202 
Abstract  The Oncereinforced random walk was introduced in the nineties as an a priori simplistic model of random walk with memory. Since then, only a few results have been proved, but very interesting features have been conjectured. During two onehour talks, I will present in detail these conjectures about the recurrencetransience of the Oncereinforced random walk and I will give an overview of the current knowledge about this model. We will see different techniques which are useful in order to study the Oncereinforced reinforced random walks on ladders, or on trees. In particular, we will eventually focus on techniques developed in a recent joint work with Andrea Collevecchio and Vladas Sidoravicius. 
S10  Convergence of random walks for trap models on disordered media 
Speaker  Professor Takashi Kumagai, Kyoto University 
Time  10:3011:30 Oct. 20 
Place  N202 
Abstract  In 2002, FontesIsopiNewman introduced a diffusion (which is now called a FIN diffusion) as a scaling limit of the 1dimensional Bouchaud trap model. It is a time change of 1dimensional Brownian motion. In this talk, we will consider more general setting and discuss convergence of random walks for trap models on disordered media. We first provide a general framework for studying such time changed processes and their discrete approximations in the case when the underlying stochastic process is strongly recurrent, in the sense that it can be described by a resistance form, as introduced by J. Kigami. We then apply the general theory to trap models on recurrent fractals and on random media such as the ErdősRényi random graph in the critical window. If time permits, we also discuss heat kernel estimates for the relevant timechanged processes. This is a joint work with D. Croydon (Warwick) and B.M. Hambly (Oxford). 
S11  Continuousstate branching processes in Levy environments 
Speaker  Professor Zenghu Li, Beijing Normal University 
Time  14:3016:30, Oct. 24 
Place  N202 
Abstract  A continuousstate branching processes in random environment (CBREprocess) is defined as the strong solution of a stochastic integral equation. The environment is determined by a Levy process with no jump less than 1. Characterizations of the quenched and annealed transition semigroups of the process can be given in terms of a backward stochastic integral equation. The process hits zero with strictly positive probability if and only if its branching mechanism satisfies Grey's condition. In that case, a characterization of the extinction probability is given using a random differential equation with singular terminal condition. The strong Feller property of the CBREprocess can be established by a coupling method. A criterion for the ergodicity of a subcricital CBREprocess with immigration can be given by an integral condition. This is a brief survey of the recent progresses in the subject. 
S12  TBA 
Speaker  Professor Kening Lu, Brigham Young University 
Time  14:3016:30, Nov. 7 
Place  N202 
AbstractTBA 
S13  Perturbative characterization of ballisticity of random walks in i.i.d. random environments 
Speaker  Professor Alejandro Ramirez, Pontificia Universidad Católica de Chile 
Time  16:3017:30 Oct. 27 
Place  N202 
Abstract  We provide a sufficient condition for ballisticity for random walks in i.i.d. random environments which are perturbations of the simple symmetric random walk in terms of the expectation and variance of the drift at a single site, extending and giving a sharper version of a result of Sznitman of 2004. Our theorem gives new examples of ballistic random walks in random environment satisfying the polynomial decay condition (P), but which do not satisfy Kalikow’s condition. This is a joint work with Santiago Saglietti. 
S14  Mathematics of Multiparticle diffusion limited aggregation 
Speaker  Professor Vladas Sidoravicius, Courant and NYUShanghai 
Time  15:3016:30 Oct. 13 
Place  N202 
Abstract  In late seventies H. Rosenstock and C. Marquardt introduced the following stochastic aggregation model on $\mathbbZ^d$: Start with particles distributed according to the product Bernoulli measure with parameter $\?$. In addition, start with a static aggregate at the origin. Nonaggregated particles move as continuoustime simple random walks obeying the exclusion rule, whereas aggregated particles do not move. The aggregate grows by attaching particles to its surface whenever a particle attempts to jump onto it. This evolution is called Multiparticle Diffusion Limited Aggregation (MDLA). Its difficult to analyze structure inspired Witten and Sander to introduce in 1981 a "simplified version" of the model with only one particle moving at a step of procedure, which became well known as celebrated DLA model. MDLA model even in dimension 1 has highly nontrivial behavior. In its random walk version (instead of exclusion process) H. Kesten and V. Sidoravicius proved that if the original density of particles is smaller than one, then the aggregate is growing sublinearly, and more than ten years later A. Sly showed that for the density larger than one it advances linearly, establishing a remarkable phase transition. In my talk I will briefly review known results and will focus on the progress in dimensions $d\geq 2$. For random walk systems A. Sly argument imply linear growth of the farmost reaching arm of the aggregate. Our main result (joint with A. Stauffer) states that for the exclusion version of the process if $d > 1$ and the initial density of particles is large enough, then with positive probability the aggregate has linearly growing arms; that is, there exists a constant $c > 0$ so that at time $t$ the aggregate contains a point of distance at least $ct$ from the origin, for all $t$. In fact it obeys certain type of the shape theorem. The key conceptual element of our analysis is the introduction and study of a new growth process. Study of this process indicates that high density MDLA belongs to KardarParisiZhang (KPZ) universality class. Very intriguing question is if in dimension $d \geq 2$ there exists similar phase transition as in dimension one, and how it affects geometric shapes of the aggregate. In other words is MDLA undergoing transition from DLA type growth (at low density) to KPZ type growth (for high density). 
S15  BSDE and SPDE with Holder continuous coefficient and applications 
Speaker  Professor Jie Xiong, University of Macau 
Time  14:3016:30, Oct. 23 
Place  N202 
Abstract  The connection between backward stochastic differential equations (BSDE) and stochastic partial differential equations (SPDE) developed by Pardoux and Peng is extended to equation with Holder continuous coefficients. As applications, uniqueness of solutions for some SPDEs are obtained. 
S16  Approximation of stable law by Stein’s method 
Speaker  Professor Lihu Xu, Universidade de Macau 
Time  15:3016:30, Oct. 25 
Place  N202 
Abstract  We will use Stein’s method to prove a general inequality which gives the convergence rate of stable law. Some examples will be studied with a comparison with the known results. The talk is based on the paper https://arxiv.org/abs/1709.00805 
S17  On regular subspaces of Dirichlet forms 
Speaker  Professor Jiangang Ying, Fudan University 
Time  09:3011:30, Oct. 28 
Place  N202 
Abstract  This talk is a survey on regular Dirichlet subspace of a given Dirichlet form. We will talk about the background and recent progress of this problem. In particular, we will focus on the representation of symmetric Dirichlet forms on real line, and regular Dirichlet subspaces and extensions of 1dim Brownian motion. More remained problems will be presented. 
S18  Multidimensional singular stochastic differential equations 
Speaker  Professor Xicheng Zhang, Wuhan University 
Time  14:3016:30, Nov. 1 
Place  N202 
Abstract  In this talk I will report some recent progress about multidimensional singular stochastic differential equations. Here the singular SDE means that the coefficients are usually in some Sobolev spaces. I will address the basic method and some technical points. In particular, most of results are based on solving the associated PDE. 