The CUNY Probability Seminar is typically held on Tuesdays from 4:15 to 5:15 pm at the CUNY Graduate Center Math Department. The exact dates, times and locations are mentioned below.

**Sept 13, 2016 at 4:15pm, Room 6494 **

Speaker: Eliran Subag, Weizmann Institute of Science Title: Critical points and the Gibbs measure of pure spherical spin glasses

Abstract: For each $N$ let $H_N(x)$ be an isotropic Gaussian field on the $N$-dimensional unit sphere, meaning that $Cov(H_N(x),H_N(y))$ is a function, say $f_N$, of the inner product of $x$ and $y$. The spherical spin glass models of statistical mechanics are exactly the class of all such sequences of random fields where one assumes in addition that $f_N = Nf$ for some $f$ independent of the dimension $N$. To investigate the intricate landscape $H_N(x)$ one may study its 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 of the behaviour of $H_N(x)$ in neighborhoods around the critical points, we obtain a detailed geometric picture for the Gibbs measure at low enough temperature: the measure concentrates on spherical “bands” around the deepest critical points. The main focus of the talk will be describing the latter and consequences of it. The talk is based on a joint work with Ofer Zeitouni.

**Sept 20m 2016, at 4:15pm, Room 6494 **Speaker: Haya Kaspi, Technion Title: TBD

**Sept 27, 2016, at 4:15pm, Room 6494 **

Speaker: Andrey Sarantsev, University of California – Santa Barbara

Title: Competing Brownian Particles

Abstract: Consider a finite or infinite system of Brownian particles on the real line. Each particle moves as a Brownian motion with drift and diffusion coefficients depending on its current rank relative to other particles. These systems were introduced in Banner, Fernholz, Karatzas (2005). Since then, extensive theory was developed for finite systems. However, infinite systems proved to be much more difficult. We survey the latest results.

**Nov 1, 2016, at 4:15pm, Room 6494 ** Speaker: Jonathon Peterson, Purdue University Title: TBD

**Nov 8, 2016, at 4:15pm, Room 6494 **

Speaker: Chiranjib Mukherjee, NYU

Title: TBD