ASYMPTOTICS OF A CUBIC SINE KERNEL DETERMINANT

T. Bothner; A. Its

doi:10.1090/spmj/1350

ASYMPTOTICS OF A CUBIC SINE KERNEL DETERMINANT

T. Bothner, A. Its

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

The one-parameter family of Fredholm determinants det(I−γK_csin), γ∈R, is studied for an integrable Fredholm operator K_csin that acts on the interval (−s,s) and whose kernel is a cubic generalization of the sine kernel that appears in random matrix theory. This Fredholm determinant arises in the description of the Fermi distribution of semiclassical nonequilibrium Fermi states in condensed matter physics as well as in the random matrix theory. By using the Riemann–Hilbert method, the large s asymptotics of det(I−γK_csin) is calculated for all values of the real parameter γ.

Original language	English
Pages (from-to)	515-565
Number of pages	51
Journal	St. Petersburg Mathematical Journal
Volume	26
DOIs	https://doi.org/10.1090/spmj/1350
Publication status	E-pub ahead of print - 6 May 2015

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© 2015 American Mathematical Society

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title = "ASYMPTOTICS OF A CUBIC SINE KERNEL DETERMINANT",

abstract = "The one-parameter family of Fredholm determinants det(I−γKcsin), γ∈R, is studied for an integrable Fredholm operator Kcsin that acts on the interval (−s,s) and whose kernel is a cubic generalization of the sine kernel that appears in random matrix theory. This Fredholm determinant arises in the description of the Fermi distribution of semiclassical nonequilibrium Fermi states in condensed matter physics as well as in the random matrix theory. By using the Riemann–Hilbert method, the large s asymptotics of det(I−γKcsin) is calculated for all values of the real parameter γ. ",

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AU - Bothner, T.

AU - Its, A.

PY - 2015/5/6

Y1 - 2015/5/6

N2 - The one-parameter family of Fredholm determinants det(I−γKcsin), γ∈R, is studied for an integrable Fredholm operator Kcsin that acts on the interval (−s,s) and whose kernel is a cubic generalization of the sine kernel that appears in random matrix theory. This Fredholm determinant arises in the description of the Fermi distribution of semiclassical nonequilibrium Fermi states in condensed matter physics as well as in the random matrix theory. By using the Riemann–Hilbert method, the large s asymptotics of det(I−γKcsin) is calculated for all values of the real parameter γ.

AB - The one-parameter family of Fredholm determinants det(I−γKcsin), γ∈R, is studied for an integrable Fredholm operator Kcsin that acts on the interval (−s,s) and whose kernel is a cubic generalization of the sine kernel that appears in random matrix theory. This Fredholm determinant arises in the description of the Fermi distribution of semiclassical nonequilibrium Fermi states in condensed matter physics as well as in the random matrix theory. By using the Riemann–Hilbert method, the large s asymptotics of det(I−γKcsin) is calculated for all values of the real parameter γ.

U2 - 10.1090/spmj/1350

DO - 10.1090/spmj/1350

M3 - Article (Academic Journal)

SN - 1061-0022

VL - 26

SP - 515

EP - 565

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

ER -

ASYMPTOTICS OF A CUBIC SINE KERNEL DETERMINANT

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