2024 Blue Ridge Probability Day

Event date: Friday, October 4, 2024

conferences »
Humpback Rocks

The inaugural Blue Ridge Probability Day will occur on Friday, October 4, 2024, in Kerchof 111, from 1:00-5:00 PM. The speakers are

1-2pm

Shalin Parekh (Maryland) - Extreme value theory for random walks in random media

The KPZ equation is a singular stochastic PDE arising as a scaling limit of various physically and probabilistically interesting models. Often this equation describes the “crossover” between Gaussian and non-Gaussian fluctuation behavior in models of interacting particles, directed polymers, or interface growth models. In this talk, I will discuss recent progress we have made in understanding the KPZ crossover for models of random walks in dynamical random media. This talk includes joint work with Sayan Das and Hindy Drillick.

2-2:30pm: Coffee break
2:30-3:30pm

Greta Panova (USC) - Algebra meets probability: Permutons from pipe dreams via TASEP

Pipe dreams are tiling models originally introduced to study objects related to the Schubert calculus and K-theory of the Grassmannian. They can also be viewed as ensembles of lattice walks with various interaction constraints. In our quest to understand what the maximal and typical algebraic objects look like, we revealed some interesting permutons. The proofs use the theory of the Totally Asymmetric Simple Exclusion Process (TASEP). Deeper connections with free fermion six-vertex models and domino tilings of the Aztec diamond allow us to describe the extreme cases of the original algebraic problem. This is based on joint work with A. H. Morales, L. Petrov, D. Yeliussizov.

3:30-4pm: Coffee break
4-5pm

Nicholas Cook (Duke) - The maximum of Poissonian log-correlated fields

In recent years there has been intense interest in extreme values of logarithmically correlated fields (LCFs), in connection with problems on Gaussian multiplicative chaos, random matrices, branching random walks, reaction-diffusion PDE, and L-functions in analytic number theory. The sharpest results are for Gaussian or nearly-Gaussian fields. On the other hand, characteristic polynomials of sparse random matrices give rise to LCFs with Poissonian tails. In earlier work with Zeitouni on permutation matrices we obtained the leading order of the maximum. I will discuss new refined results on the maximum for a related class of random trigonometric polynomials with Poissonian tails. We find the sub-leading order behavior is significantly different from the ubiquitous “Bramson correction” term for Gaussian LCFs, and can be modeled by a branching random walk with a randomly time-varying offspring distribution. Based on joint work with Haotian Gu (Duke).

Last updated: Friday, September 27, 2024