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.)
á 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.
á 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.
á 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
á 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.
á 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.
á 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.
á Thursday February 8, 2018, 10am
Yumeng Zhang, Stanford University
á Thursday March 8, 2018, 10am
Georg Menz, UCLA
á Thursday March 15, 2018, 10am
Karl Liechty, De Paul University
á Thursday May 3, 2018, 10am
Dan Romik, UC Davis