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On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo–Miwa–Ueno differential

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On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo–Miwa–Ueno differential. / Bothner, Thomas; Its, Alexander; Prokhorov, Andrei.

In: ADVANCES IN MATHEMATICS, Vol. 345, 17.03.2019, p. 483–551.

Research output: Contribution to journalArticle

Harvard

Bothner, T, Its, A & Prokhorov, A 2019, 'On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo–Miwa–Ueno differential', ADVANCES IN MATHEMATICS, vol. 345, pp. 483–551. https://doi.org/10.1016/j.aim.2019.01.025

APA

Bothner, T., Its, A., & Prokhorov, A. (2019). On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo–Miwa–Ueno differential. ADVANCES IN MATHEMATICS, 345, 483–551. https://doi.org/10.1016/j.aim.2019.01.025

Vancouver

Bothner T, Its A, Prokhorov A. On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo–Miwa–Ueno differential. ADVANCES IN MATHEMATICS. 2019 Mar 17;345:483–551. https://doi.org/10.1016/j.aim.2019.01.025

Author

Bothner, Thomas ; Its, Alexander ; Prokhorov, Andrei. / On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo–Miwa–Ueno differential. In: ADVANCES IN MATHEMATICS. 2019 ; Vol. 345. pp. 483–551.

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@article{2c3d02280ae94c2a99ac1c44ec1a10f1,
title = "On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo–Miwa–Ueno differential",
abstract = "Several distribution functions in the classical unitarily invari-ant matrix ensembles are prime examples of isomonodromic tau functions as introduced by Jimbo, Miwa and Ueno (JMU) in the early 1980s [45]. Recent advances in the theory of tau functions [41], based on earlier works of B. Malgrange and M. Bertola, have allowed to extend the original Jimbo–Miwa–Ueno differential form to a 1-form closed on the full space of extended monodromy data of the underlying Lax pairs. This in turn has yielded a novel approach for the asymptotic evaluation of isomonodromic tau functions, in-cluding the exact computation of all relevant constant factors. We use this method to efficiently compute the tail asymp-totics of soft-edge, hard-edge and bulk scaled distribution and gap functions in the complex Wishart ensemble, provided",
keywords = "Action integrals, Isomonodromic tau-functions, Poisson statistics, Tail asymptotics, Thinned LUE process, Weibull statistics",
author = "Thomas Bothner and Alexander Its and Andrei Prokhorov",
year = "2019",
month = mar,
day = "17",
doi = "10.1016/j.aim.2019.01.025",
language = "English",
volume = "345",
pages = "483–551",
journal = "ADVANCES IN MATHEMATICS",
issn = "0001-8708",
publisher = "ACADEMIC PRESS INC",

}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo–Miwa–Ueno differential

AU - Bothner, Thomas

AU - Its, Alexander

AU - Prokhorov, Andrei

PY - 2019/3/17

Y1 - 2019/3/17

N2 - Several distribution functions in the classical unitarily invari-ant matrix ensembles are prime examples of isomonodromic tau functions as introduced by Jimbo, Miwa and Ueno (JMU) in the early 1980s [45]. Recent advances in the theory of tau functions [41], based on earlier works of B. Malgrange and M. Bertola, have allowed to extend the original Jimbo–Miwa–Ueno differential form to a 1-form closed on the full space of extended monodromy data of the underlying Lax pairs. This in turn has yielded a novel approach for the asymptotic evaluation of isomonodromic tau functions, in-cluding the exact computation of all relevant constant factors. We use this method to efficiently compute the tail asymp-totics of soft-edge, hard-edge and bulk scaled distribution and gap functions in the complex Wishart ensemble, provided

AB - Several distribution functions in the classical unitarily invari-ant matrix ensembles are prime examples of isomonodromic tau functions as introduced by Jimbo, Miwa and Ueno (JMU) in the early 1980s [45]. Recent advances in the theory of tau functions [41], based on earlier works of B. Malgrange and M. Bertola, have allowed to extend the original Jimbo–Miwa–Ueno differential form to a 1-form closed on the full space of extended monodromy data of the underlying Lax pairs. This in turn has yielded a novel approach for the asymptotic evaluation of isomonodromic tau functions, in-cluding the exact computation of all relevant constant factors. We use this method to efficiently compute the tail asymp-totics of soft-edge, hard-edge and bulk scaled distribution and gap functions in the complex Wishart ensemble, provided

KW - Action integrals

KW - Isomonodromic tau-functions

KW - Poisson statistics

KW - Tail asymptotics

KW - Thinned LUE process

KW - Weibull statistics

UR - http://www.scopus.com/inward/record.url?scp=85059934857&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2019.01.025

DO - 10.1016/j.aim.2019.01.025

M3 - Article

VL - 345

SP - 483

EP - 551

JO - ADVANCES IN MATHEMATICS

JF - ADVANCES IN MATHEMATICS

SN - 0001-8708

ER -

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