# UC San Diego Probability Seminar   2018-2019

#### Seminar Information

Thursdays, 11am   AP&M 6402
University of California, San Diego
La Jolla, CA 92093-0112
Map

Organizer:    Todd Kemp
E-mail:          tkemp@math.ucsd.edu

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## Fall 2018 Schedule

Sept 27    Nikhil Srivastava, UC Berkeley
 Concentration for Sums of Random Matrices with Markov Dependence There are many well-known concentration results for sums of independent random matrices, e.g. those of Rudelson, Ahlswede-Winter, Tropp, and Oliveira. We move beyond the independent setting, and prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a random walk on an reversible Markov chain, confirming a conjecture due to Wigderson and Xiao. Our proof is based on a new multi-matrix extension of the Golden-Thompson inequality which follows from complex interpolation methods. (Joint work with A. Garg, Y. Lee, and Z. Song.)

Oct 25    Li-Cheng Tasi, Columbia University
 Lower-tail large deviations of the KPZ equation Regarding time as a scaling parameter, we prove the one-point, lower tail Large Deviation Principle (LDP) of the KPZ equation, with an explicit rate function. This result confirms existing physics predictions. We utilize a formula from [Borodin Gorin 16] to convert LDP of the KPZ equation to calculating an exponential moment of the Airy point process, and analyze the latter via stochastic Airy operator and Riccati transform.

Nov 8    Joshua Frisch, Caltech
 Proximal actions, Strong amenability, and infinite conjugacy class groups. A topological dynamical system (i.e. a group acting by homeomorphisms on a compact topological space) is said to be proximal if for any two points $p$ and $q$ we can simultaneously push them together i.e. there is a sequence $g_n$ such that $\lim g_n(p)=\lim g_n (q)$. In his paper introducing the concept of proximality Glasner noted that whenever $\mathbb{Z}$ acts proximally that action will have a fixed point. He termed groups with this fixed point property "strongly amenable" and showed that non-amenable groups are not strongly amenable and virtually nilpotent groups are strongly amenable. In this talk I will discuss recent work precisely characterizing which (countable) groups are strongly amenable.

Nov 15    Noah Forman, University of Washington
 The diffusion analogue to a tree-valued Markov chain In '99, David Aldous conjectured that a certain natural "random walk" on the space of binary combinatorial trees should have a continuum analogue, which would be a diffusion on the Gromov-Hausdorff space of continuum trees. This talk discusses ongoing work by F-Pal-Rizzolo-Winkel that has recently verified this conjecture with a path-wise construction of the diffusion. This construction combines our work on dynamics of certain projections of the combinatorial tree-valued random walk with our previous construction of interval-partition-valued diffusions.

## "Winter" 2019 Schedule

Jan 10    Tom Kurtz, University of Wisconsin
 TBA

## Spring 2019 Schedule

Apr 4    Elizabeth and Mark Meckes, Case Western University
 TBA