**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.)*

**Fall 2017**

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.

**Winter 2018**

á Thursday February
8, 2018, 10am

**Yumeng**** Zhang, Stanford
University**

**Title:**

**Abstract: **

á Thursday March
8, 2018, 10am

**Georg Menz, UCLA**

**Title:**

**Abstract: **

á Thursday March
15, 2018, 10am

**Karl Liechty, De Paul University**

**Title:**

**Abstract: **

**Spring 2018**

á Thursday May 3,
2018, 10am

**Dan Romik, UC Davis**

**Title:**

**Abstract: **