C O L U M B I A /
C O U R A N T
P R O B A B I L I T Y
S E M I N A R
S E R I E S

Joint Columbia-NYU probability talks, organized by probabilists from both institutions.

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Friday October 14th, Courant institute, Warren Weaver Hall, 512

- 9.30-10.30am
** Eliran Subag ** (Weizmann).
*Critical points and the Gibbs measure of pure spherical spin glasses*

Mathematically, spherical spin glasses are smooth Gaussian fields on the N-dimensional sphere. To investigate their intricate landscape one may study the critical points and values. Focusing on the pure p-spin models, I will review recent developments concerning the distribution of the number of critical values at a given height and the associated extremal point process. Combining these results with a local investigation around the critical points yields a detailed geometric picture for the Gibbs measure at low enough temperature: the measure concentrates on spherical "bands" around the deepest critical points. The talk will focus on the latter and consequences of it.
The talk is based on a joint work with Ofer Zeitouni.

- 10.30-11am
**Coffee break**
* *

- 11am-12pm
** Li Cheng Tsai ** (Columbia U.).
* Interacting particle systems with moving boundaries*

In this talk we will survey a few one-dimensional particle systems with a moving boundary. This includes the infinite Atlas model, Aldous' up-the-river problem, and a modified one-dimensional Diffusion Limited Growth. In these systems, particles perform independent Brownian motions or random walks, and interact only through the boundary via rank-based drift and/or absorption. We will explain how connecting these systems to PDE and Stochastic PDE helps to solve problems regarding large time asymptotics. For systems with absorption, we will demonstrate a new method of utilizing the flux condition to bypass the loss of control on local equilibrium.
This talk is based on joint work with Amir Dembo and Wenpin Tang.

- 12-1pm
** Robin Pemantle ** (U. Penn).
* Recursions that mix +/x with Max/Min*.

This talk concerns several probability models whose
analyses involve distributional recursions that
mix algebraic operations (plus or times) with
either Max or Min. Examples include random Boolean
functions, random min-plus functions, and LIS for
tropical random walks.