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arXiv · 1807.11387

The sine process under the influence of a varying potential

Thomas Bothner·Percy Deift·Alexander Its·Igor Krasovsky
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Abstract

We review the authors' recent work \cite{BDIK1,BDIK2,BDIK3} where we obtain the uniform large $s$ asymptotics for the Fredholm determinant $D(s,γ):=\det(I-γK_s\upharpoonright_{L^2(-1,1)})$, $0\leqγ\leq 1$. The operator $K_s$ acts with kernel $K_s(x,y)=\sin(s(x-y))/(π(x-y))$ and $D(s,γ)$ appears for instance in Dyson's model \cite{Dyson2} of a Coulomb log-gas with varying external potential or in the bulk scaling analysis of the thinned GUE \cite{BP}.

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Thomas Bothner, Percy Deift, Alexander Its, Igor Krasovsky. 2018-07-30. The sine process under the influence of a varying potential. https://doi.org/10.1063/1.5050394

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