The sine process under the influence of a varying potential

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2018-09
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English
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Abstract

We review the authors’ recent work where we obtain the uniform large s asymptotics for the Fredholm determinant D(s,γ)≔det(I−γKs↾L2(−1,1)), 0 ≤ γ ≤ 1. The operator Ks acts with kernel Ks(x, y) = sin(s(x − y))/(π(x − y)), and D(s, γ) appears for instance in Dyson’s model of a Coulomb log-gas with varying external potential or in the bulk scaling analysis of the thinned Gaussian unitary ensemble.

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Bothner, T., Deift, P., Its, A., & Krasovsky, I. (2018). The sine process under the influence of a varying potential. Journal of Mathematical Physics, 59(9), 091414. https://doi.org/10.1063/1.5050394
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Journal of Mathematical Physics
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