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Probability

Organizers: Amir Dembo (Autumn) & Eric Thoma (Spring)

Upcoming Events

Feb
24
Date3:15 PM
Location
Sequoia 200
Speaker
Riddhipratim Basu (ICTS, India)

I shall discuss first-passage percolation on Cayley graphs of Gromov hyperbolic groups under mild conditions on the passage time distribution. Appealing to deep geometric and topological facts about hyperbolic groups and their boundaries, several questions become more tractable in this set-up…

Feb
24
Date4:30 PM
Location
Sequoia 200
Speaker
Pierfrancesco Urbani (U. Paris-Saclay)
Mar
31
Date4:00 PM
Location
Sequoia 200
Speaker
Youngtak Sohn (Brown)

Past Events

Feb
10
Date4:00 PM
Location
Sequoia 200
Speaker
Reza Gheissari (Northwestern)

The (d+1)D solid-on-solid model is a simple model of integer-valued height functions that approximates the low-temperature interface of an Ising model. When $d\geq 2$, with zero-boundary conditions, at low temperatures the surface is localized about height 0, but when constrained to take only…

Feb
03
Date4:00 PM
Location
Sequoia 200
Speaker
Mehtaab Sawhney (Columbia)

Let A be an n by n matrix with iid Ber(d/n) entries. We show that the empirical measure of the eigenvalues converges, in probability, to a deterministic distribution. The proof involves incrementally exposing the randomness of the underlying matrix and studying the evolution of the singular…

Jan
27
Date4:00 PM
Location
Sequoia 200
Speaker
Amol Aggarwal (Columbia)

Lévy matrices are symmetric random matrices whose entries are in the domain of attraction of an \alpha stable law. For \alpha < 1, it had been predicted that these matrices exhibit an Anderson transition, also called a mobility edge, a point in the spectrum where eigenvector behavior sharply…

Jan
21
Date4:30 PM
Location
Pigott (01-260) 113
Speaker
Brice Huang (MIT)

Optimizing high-dimensional functions generated from random data is a central problem in modern statistics and machine learning. As these objectives are highly non-convex, the maximum value reachable by efficient algorithms is usually smaller than the maximum value that exists, and…

Jan
13
Date4:00 PM
Location
Sequoia 200
Speaker
Eric Thoma (Stanford)

The Coulomb gas is a statistical physics model consisting of N particles interacting with electrostatic repulsion and with a global confining potential. I will show how a certain subharmonic structure associated with the k-point function arises. This structure implies new bounds on quantities…

Jan
06
Date4:00 PM
Location
Sequoia 200
Speaker
Allan Sly (Princeton)

Last May I spoke about a series of multi-scale arguments to establish scaling relations for rotationally invariant first passage percolation in the plane. In this talk I will discuss how these methods can be used to establish the chaotic nature of the optimal path, that is, after a small…

Dec
02
Date4:00 PM
Location
Sequoia Hall 200
Speaker
Tianqi Wu (Technion)

Branching Brownian motion (BBM) is a classical probabilistic model that has "log-correlated" behavior. Its limiting extremal process has been derived to be that of a randomly shifted clustered Poisson point process with an exponential intensity (Aidekon-Berestycki-Brunet-Shi; Arguin-Bovier-…

Nov
18
Date4:00 PM
Location
Sequoia 200
Speaker
Shuangping Li (Stanford Statistics)

We show that the shortest s-t path problem has the overlap-gap property in (i) sparse G(n,p) graphs and (ii) complete graphs with i.i.d. exponential edge weights. Furthermore, we demonstrate that in sparse G(n,p) graphs, shortest path is solved by O(log n)-degree polynomial estimators, and a…

Nov
11
Date4:00 PM
Location
Sequoia 200
Speaker
Eliran Subag (Weizmann Institute)

Given a Gaussian energy function H(x) and another random process O(x) (an observable) both defined on the same configuration space, what is the law of O(y) for y sampled from the Gibbs measure associated to H(x)? We will see the answer to this question in the high-temperature phase in a general…

Nov
04
Date4:00 PM
Location
Sequoia 200
Speaker
Dor Elboim (Stanford)

A self-interacting random walk is a random process evolving in an environment which depends on its history. In this talk, we will discuss a few examples of these walks including the Lorentz gas, the mirror walk and the cyclic walk in the interchange process. I will present a method to analyze…