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Critical asymptotics for Toeplitz determinants and the Painlevé V equation

Fri 03 May 2013, 14:00

Tom Claeys
Université Catholique de Louvain

Mathematical Physics

Organiser: Nina Snaith

ABSTRACT
I will discuss asymptotic expansions for Toeplitz determinants corresponding
to symbols depending on a parameter t. For t positive, the symbols
have two Fisher-Hartwig singularities, but as t tends to zero, the singularities merge, and at t=0, there is only one singularity left.
Double scaling asymptotics for the determinants as n tends to infinity and simultaneously t tends to zero can be expressed in terms of a solution to the fifth Painlevé equation.
The talk will be based on joint work with Igor Krasovsky.