UCSD Probability Seminar, 2017-2018


The probability seminar meets at 10am on Thursdays in AP&M 6402, unless specifically indicated otherwise. Please send any inquiries to the organizer

T. Zheng ( tzheng2 at math dot ucsd dot edu.)


Winter 2018


  Thursday February 8, 2018, 10am

Yumeng Zhang, Stanford University

Title: Rapid mixing of Glauber dynamics on hypergraph independent set


Abstract: Independent sets in hypergraphs can be encoded as 0-1 configurations on the set of vertices such that each hyperedge is adjacent to at least one 0. This model has been studied in the CS community for its large gap between efficient MCMC algorithms (previously d <(k-1)/2) and the conjectured onset of computational hardness (d > O(2^{k/2}) ), where d is the largest degree of vertices and k is the minimum size of hyperedges. In this talk we use a percolation approach to show that the Glauber dynamics is rapid mixing for d < O(2^{k/2} ), closing the gap up to a multiplicative constant.

This is joint work with Jonathan Hermon and Allan Sly.




  Thursday February 15, 2018, 10am

Leonid Petrov, University of Virginia


Title: Nonequilibrium particle systems in inhomogeneous space


Abstract: I will discuss stochastic interacting particle systems in the KPZ universality class evolving in one-dimensional inhomogeneous space. The inhomogeneity means that the speed of a particle depends on its location. I will focus on integrable examples of such systems, i.e., for which certain observables can be written in exact form suitable for asymptotic analysis. Examples include a continuous-space version of TASEP (totally asymmetric simple exclusion process), and the pushTASEP (=long-range TASEP). For integrable systems, density limit shapes can be described in an explicit way. We also obtain asymptotics of fluctuations, in particular, around slow bonds and infinite traffic jams caused by slowdowns.





  Thursday March 8, 2018, 10am

Georg Menz, UCLA

Title:  A quantitative theory of the hydrodynamic limit


Abstract: The hydrodynamic limit of the Kawasaki dynamics states that a certain stochastic evolution of a lattice system converges macroscopically to a deterministic non-linear heat equation. We will discuss how the statement of the hydrodynamic limit can be made quantitative. The key step is to introduce an additional evolution on a mesoscopic scale that emerges from projecting the microscopic observables onto splines. The hydrodynamic limit is then deduced in two steps. In the first step one shows the convergence of the microscopic to the mesoscopic evolution and in the second step one deduces the convergence of the mesoscopic to the macroscopic evolution.

The talk is about a joint work with Deniz Dizdar, Felix Otto and Tianqi Wu.





  Thursday March 15, 2018, 10am

Karl Liechty, De Paul University

Title: Tacnode processes, winding numbers, and Painleve II


Abstract: Abstract: I will discuss a model of nonintersecting Brownian bridges on the unit circle, which produces quite a few universal determinantal processes as scaling limits. I will focus on the tacnode process, in which two groups of particles meet at a single point in space-time before separating, and introduce a new version of the tacnode process in which a finite number of particles "switch sides" before the two groups separate. We call this new process the k-tacnode process, and it is defined by a kernel expressed in terms of a system of tau-functions for the Painleve II equation. Technically, our model of nonintersecting Brownian bridges on the unit circle is studied using a system of discrete orthogonal polynomials with a complex (non-Hermitian) weight, so I'll also discuss some of the analytical obstacles to that analysis.
This is joint work with Dong Wang and Robert Buckingham




Spring 2018



  Thursday April 19, 2018, 10am

Nick Cook, UCLA






  Thursday May 3, 2018, 10am

Lucien Beznea, IMAR






  Thursday May 10, 2018, 10am

Pascal Maillard, Universit Paris-Sud





  Thursday June 7, 2018, 10am

Dan Romik, UC Davis






Fall 2017


Thursday, Oct 5, 2017, 10am

Jean-Dominique Deuschel, TU Berlin


Title: Random walks in dynamical balanced environment 


Abstract: We prove a quenched invariance principle and local limit theorem for a random walk in an ergodic balanced time dependent environment on the lattice. Our proof relies on the parabolic Harnack inequality for the adjoint operator. This is joint work with X. Guo.


Thursday, Oct 12, 2017, 10am

Pierre-Olivier Goffard, UC Santa Barbara


Title: Boundary Crossing Problems with Applications to Risk Management.


Abstract: Many problems in stochastic modeling come down to study the crossing time of a certain stochastic process through a given boundary, lower or upper. Typical fields of application are in risk theory, epidemic modeling, queueing, reliability and sequential analysis. The purpose of this talk is to present a method to determine boundary crossing probabilities linked to stochastic point processes having the order statistic property. A very well-known boundary crossing result is revisited, a detailed proof is given. the same arguments may be used to derive results in trickier situations. We further discuss the practical implications of this classical.

Thursday, Oct 19, 2017, 10am

Omer Tamuz, Caltech


Title: Large deviations in social learning


Abstract: Models of information exchange that originate from economics provide interesting questions in probability. We will introduce some of these models, discuss open questions, and explain some recent results.

Joint with Wade Hann-Caruthers, Matan Harel, Vadim Martynov, Elchanan Mossel and Philipp Strack



Thursday, Nov 2, 2017, 10am

Qiang Zeng, Northwestern University


Title: The Sherrington-Kirkpatrick model is Full-step Replica Symmetry Breaking at zero temperature


Abstract: Starting in 1979, the physicist Giorgio Parisi wrote a series of ground breaking papers introducing the idea of replica symmetry breaking, which allowed him to predict a solution for the Sherrington-Kirkpatrick (SK) model by breaking the symmetry of replicas infinitely many times. This is known as full-step replica symmetry breaking (FRSB). In this talk, we will provide a mathematical proof of Parisi's FRSB prediction at zero temperature for the more general mixed p-spin model. More precisely, we will show that the functional order parameter of this model is not a step function. This talk is based on joint work with Antonio Auffinger and Wei-Kuo Chen.



  Thursday, Nov 30, 2017, 10am

Tom Alberts, University of Utah


Title: Geometric Methods for Last Passage Percolation


Abstract:  In an attempt to generalize beyond solvable methods of analysis for last passage percolation, recently Eric Cator (Radboud University, Nijmegen) and I have started analyzing the piecewise linearity of the last passage model. The tools we use to this point are purely geometric, but have the potential advantage that they can be used for very general choices of random inputs. I will describe the very pretty geometry of the last passage model, our work in progress to use it to produce probabilistic information, and some connections to algebraic geometry.




  Thursday, Dec 7, 2017, 10am

Anas Rahman, University of Melbourne

Title: Random Matrices and Loop Equations

Abstract: I will begin by introducing the Gaussian, Laguerre and Jacobi ensembles and their corresponding eigenvalue densities. The moments of these eigenvalue densities are generated by the corresponding resolvent, R(x). When investigating large matrices of size N, it is natural to expand R(x) as a series in 1/N, as N tends to infinity. The loop equation formalism enables one to compute R(x) to any desired order in 1/N via a triangular recursive system. This formalism is equivalent to the topological recursion, the Schwinger-Dyson equations and the Virasoro constraints, among other things. The loop equations provide a relatively accessible entry-point to these topics and my derivation will rely on nothing more than integration by parts, as Aomoto applied to the Selberg integral. Time permitting, I may also explore links to the topological recursion and/or some combinatorics.


All original results will be from joint work with Peter Forrester and Nicholas Witte.