Hariet Walsh

will speak on

Inhomogeneous random growth in half space and solutions of Painlevé equations

Time: 3:00PM
Date: Tue 24th September 2024
Location: E0.32 (beside Pi restaurant) [map]

Further information

Abstract: I will talk about a model of two dimensional random growth (namely, polynuclear growth) which can be translated into a probability law on integer partitions (by way of the RSK algorithm). As a consequence, we can find exact expressions for statistics of this model with algebraic tools, and compute fine asymptotics. I will focus on a model in half space with external sources driving growth at the edges, and present a new asymptotic distribution governing its interface fluctuations which interpolates between different universal Tracy—Widom distributions from random matrix theory, and encodes solutions of the Painlevé II differential equation. Our approach uses connections between symmetric functions, matrix integrals, and Hankel determinants, plus a Riemann—Hilbert problem. Based on joint work with Mattia Cafasso, Alessandra Occelli and Daniel Ofner.

I will talk about a model of two dimensional random growth (namely, polynuclear growth) which can be translated into a probability law on integer partitions (by way of the RSK algorithm). As a consequence, we can find exact expressions for statistics of this model with algebraic tools, and compute fine asymptotics. I will focus on a model in half space with external sources driving growth at the edges, and present a new asymptotic distribution governing its interface fluctuations which interpolates between different universal Tracy—Widom distributions from random matrix theory, and encodes solutions of the Painlevé II differential equation. Our approach uses connections between symmetric functions, matrix integrals, and Hankel determinants, plus a Riemann—Hilbert problem. Based on joint work with Mattia Cafasso, Alessandra Occelli and Daniel Ofner.

https://ucd-ie.zoom.us/j/63693153981

(This talk is part of the Analysis series.)

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