Research output: Contribution to journal › Article

**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.

Research output: Contribution to journal › Article

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

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

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

@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",

}

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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