We review the authors' recent work where we obtain the uniform large s asymptotics for the Fredholm determinant D(s, gamma) := det(I - gamma K-s up arrow L-2(-1, 1)), 0 <= y <= 1. The operator K-s acts with kernel K-s(x, y) = sin(s(x - y))/(pi(x - y)), and D(s, gamma) 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. Published by AIP Publishing.
The sine process under the influence of a varying potential / Bothner, Thomas; Deift, Percy; Its, Alexander; Krasovsky, Igor. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 59:9(2018), pp. 1-6. [10.1063/1.5050394]
The sine process under the influence of a varying potential
Bothner, Thomas;Its, Alexander;Krasovsky, Igor
2018-01-01
Abstract
We review the authors' recent work where we obtain the uniform large s asymptotics for the Fredholm determinant D(s, gamma) := det(I - gamma K-s up arrow L-2(-1, 1)), 0 <= y <= 1. The operator K-s acts with kernel K-s(x, y) = sin(s(x - y))/(pi(x - y)), and D(s, gamma) 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. Published by AIP Publishing.| File | Dimensione | Formato | |
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