The CUNY Probability Seminar is typically held on Tuesdays from 4:15 to 5:15 pm at the CUNY Graduate Center Math Department in room 5417. The exact dates, times and locations are mentioned below. If you want to talk at the seminar, or want to be added to/removed from the seminar mailing list, then please contact the Seminar Coordinator.

*Louis-Pierre Arguin (https://arguin.commons.gc.cuny.edu/*)

## Seminar Schedule:

**Tuesday, September 3, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Nicola Kistler, Frankfurt**

**Title: **From Parisi to Boltzmann

**Abstract: **I will present a novel framework for the analysis of (mean field) disordered systems,variational in nature and abiding to the principles of classical statistical mechanics, which allows to clarify a number of puzzles posed by the Parisi theory. Time permitting, I will also discuss some of the inconsistencies of the alternative approach to spin glasses initiated by Thouless, Anderson, and Palmer. *Joint with Goetz Kersting, Adrien Schertzer (Frankfurt) and Marius A. Schmidt (Basel). *

**Tuesday, September 10, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Guillaume Dubach, CUNY**

**Title: **Words of non-Hermitian random matrices

**Abstract: **Words of non-Hermitian matrices with complex Gaussian entries can be studied using a topological expansion formula, also known as genus expansion. This results in a generalization of what is known for products of i.i.d. complex Ginibre matrices on the one hand, and powers of one such matrix on the other hand. For instance, the empirical distribution of singular values of any word is shown to converge to a Fuss-Catalan distribution whose parameter only depends on the length of the word. This can be extended to matrices with i.i.d. non-Gaussian entries, band matrices, and sparse matrices with optimal sparsity parameter. (Joint work with Yuval Peled.)

**Tuesday, September 17, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Konstantin Matetski, Columbia**

**Title: Convergence of finite-range weakly asymmetric exclusion processes on a ring.**

**Abstract: **We consider a spatially periodic growth model built from a weakly asymmetric exclusion process with finite-range jumps and rates depending locally on a configuration of particles. In general, invariant measures of the model are unknown. We prove that after diffusive rescaling and renormalization this model converges to the Hopf-Cole solution of the KPZ equation driven by a Gaussian space-time white noise. In particular, this result confirms that the KPZ scaling theory, which predicts the constants characterizing the scaling limit, holds also in the case when invariant measures are unknown.

**Tuesday, September 24, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Michel Pain, NYU**

**Title: Derrida-Retaux model: from discrete to continuous time**

**Abstract: **Derrida-Retaux model is a simple hierarchical renormalization model, originally

introduced by Collet et al., that leads to many surprisingly tough questions. Some of them have been solved recently, but many others are still open. In order to answer these questions, with Yueyun Hu and Bastien Mallein, we introduced a continuous-time version of the model, which yields an exactly solvable family of solutions. We will discuss the results obtained on this model, focusing on the behavior at criticality, where a growth-fragmentation process appears as scaling limit.

**Tuesday, October 1, 2019**

**No meeting**

**Tuesday, October 8, 2019**

**No meeting**

**Tuesday, October 15, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Jiaming Xia, UPenn**

**Title: Exponential Decay of Correlations in 2-Dimensional Random Field Ising Model**

**Abstract**: We consider the random field Ising model on Z^2 with external field i.i.d. N(0,\epsilon). I will present a recent result that under nonnegative temperatures, the effect of boundary conditions at distance N away on the magnetization in a finite box decays exponentially. This talk is based on the joint work with Prof. Jian Ding.

**Tuesday, October 22, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Tobias Johnson, College of Staten Island CUNY**

**Title: Two-type diffusion limited annihilating systems**

**Abstract:** In the two-type DLAS process, we place particles of two types on a graph and let them move randomly. When two particles of opposite type meet each other, both annihilate. The most basic question is to determine the density of particles at time t. When the two particle types jump at the same rate and have equal initial density, Bramson and Lebowitz proved that on the d-dimensional lattice, the density decays at rate t^(-d/4) for d=1, 2, 3 and at rate t^(-1) when d is 4 or greater, as was long conjectured by physicists. When the particle types jump at different rates, much less is known. We prove some results in these cases on lattices and on directed trees. The process on trees has some resemblance to the Derrida-Retaux hierarchical renormalization model. Joint work with Michael Damron, Matthew Junge, Hanbaek Lyu, and David Sivakoff.

**Tuesday, October 29, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Oanh Nguyen, Princeton**

**Title: Distribution of roots of random functions**

**Abstract: **The study of random functions has been investigated for many decades with classical results by Kac, Littlewood-Offord, Erdos-Offord, etc. In this talk, we will discuss these results together with recent developments and open problems in the field. We also discuss a general framework to prove universality results for correlation functions of the roots and apply it to study various questions on random polynomials, random trigonometric functions, and random eigenfunctions. Using these universality results, we estimate the number of nodal intersections and the number of real roots. We also show that the number of real roots satisfies the Central Limit Theorem.

This talk is based on several joint papers with Mei-Chu Chang, Yen Do, Hoi Nguyen, and Van Vu.

**Tuesday, November 5, 2019, 4:15-5:15**

**Room 5417**

**Speaker: TBA**

**Title: **

**Abstract:**

**Tuesday, November 12, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Emma Bailey, Bristol**

**Title: Unitary, Symplectic, and Orthogonal Moments of Moments**

**Abstract: **The study of random matrix moments of moments has connections to number theory, combinatorics, and log-correlated fields. Our results give the leading order of these functions for integer moments parameters by exploiting connections with Gelfand-Tsetlin patterns. This is joint work with Jon Keating and Theo Assiotis.

**Tuesday, November 19, 2019, 4:15-5:15**

**No meeting. Northeast Probability Seminar November 21-22**

**Tuesday, November 26, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Chris Janjigian, Utah**

**Title:** The Busemann process and geometry of geodesics in directed last passage percolation

**Abstract:** We consider the geometric structure of the collection of all semi-infinite geodesics in last passage percolation on the square lattice, both for general weights and in the solvable setting. Coalescence properties of geodesics are shown to be equivalent to analytic properties of the Busemann functions viewed as a stochastic process in the direction parameter. As an application, we give a complete description of all semi-infinite geodesics in the solvable exponential model and discuss some interesting geometric consequences. Joint work with Firas Rassoul-Agha and Timo Seppäläinen.

**Tuesday, December 3, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Jean-Christophe Mourrat, NYU**

**Title: Mean-field disordered systems and Hamilton-Jacobi equations**

**Abstract:** Spin glasses are the most basic examples of disordered systems of statistical mechanics with mean-field interactions. The infinite-volume limit of their free energies are described by the celebrated Parisi formula. I will describe a connection between this result and certain Hamilton-Jacobi equations. The talk will then mostly focus on a simpler setting arising from the problem of infering a large rank-one matrix, in which the corresponding Hamilton-Jacobi equation is posed in a finite-dimensional space.

**Tuesday, December 10, 2019, 4:15-5:15**

**Room 5417**

**Speaker: Robert Hough, Stony Brook**

**Title: Mixing and stabilization in the abelian sandpile model**

**Abstract: **In the abelian sandpile model on a finite graph G = (V, E) the states consist of an allocation of chips at each non-sink vertex. If the number of chips at a vertex is at least the degree, the vertex topples, passing one chip to each neighbor; any chip which falls on the sink is lost from the model. Sandpile dynamics consist of dropping a chip on a uniformly random vertex and performing any available topplings. In joint work with Jerison and Levine, we have determined the asymptotic mixing time and proved a cut-off phenomenon for sandpile dynamics on the discrete torus $(\mathbb{Z}/n\mathbb{Z})^2$ with nearest neighbor edges and a single sink. We also consider the stabilization problem for i.i.d. sandpiles on \mathbb{Z}^2. In joint work with Hyojeong Son, we prove a cut-off phenomenon for sandpile dynamics on growing pieces of plane or space tilings given periodic or open boundary conditions. In two dimensions, we show that the asymptotic mixing time is the same with periodic and open boundary conditions. In 4 dimensions, we show that on the D4 lattice, the open boundary condition causes the model to mix more slowly asymptotically.