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SUMMARY:Harriet Walsh: Inhomogeneous random growth in half space and solut
ions of integrable equations
DTSTART:20240514T083000Z
DTEND:20240514T093000Z
DTSTAMP:20240622T131900Z
UID:indico-event-11588@indico.math.cnrs.fr
DESCRIPTION:I will talk about models of two dimensional random growth (nam
ely\, polynuclear growth) which can be translated into probability laws on
integer partitions by way of the RSK algorithm. As a consequence\, we can
study their asymptotic statistics with algebraic tools. I will focus on a
model in half space with external sources driving growth at the edges\, a
nd present a new asymptotic distribution governing its interface fluctuati
ons which interpolates between different universal Tracy-Widom distributio
ns from random matrix theory\, and encodes solutions of the PainlevĂ© II i
ntegrable differential equation. Our approach uses connections between sym
metric functions\, matrix integrals\, Hankel determinants\, and a Riemann-
Hilbert problem. Based on joint work with Mattia Cafasso\, Alessandra Occe
lli and Daniel Ofner.\n\nhttps://indico.math.cnrs.fr/event/11588/
LOCATION:Salle 318 (IMB)
URL:https://indico.math.cnrs.fr/event/11588/
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