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.
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.