The local universality of Muttalib-Borodin ensembles when the parameter theta is the reciprocal of an integer

Molag L (2021)
Nonlinearity 34(5): 3485-3564.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
The Muttalib-Borodin ensemble is a probability density function for n particles on the positive real axis that depends on a parameter. and a weight w. We consider a varying exponential weight that depends on an external field V. In a recent article, the large n behavior of the associated correlation kernel at the hard edge was found for theta = 1/2, where only few restrictions are imposed on V. In the current article we generalize the techniques and results of this article to obtain analogous results for theta = 1/r, where r is a positive integer. The approach is to relate the ensemble to a type II multiple orthogonal polynomial ensemble with r weights, which can then be related to an (r + 1) x ( r + 1) Riemann-Hilbert problem. The local parametrix around the origin is constructed using Meijer G-functions. We match the local parametrix around the origin with the global parametrix with a double matching, a technique that was recently introduced.
Stichworte
Riemann-Hilbert problems; multiple orthogonal polynomials; Meijer; G-functions; biorthogonal ensembles; steepest descent analysis
Erscheinungsjahr
2021
Zeitschriftentitel
Nonlinearity
Band
34
Ausgabe
5
Seite(n)
3485-3564
ISSN
0951-7715
eISSN
1361-6544
Page URI
https://pub.uni-bielefeld.de/record/2955110

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Molag L. The local universality of Muttalib-Borodin ensembles when the parameter theta is the reciprocal of an integer. Nonlinearity. 2021;34(5):3485-3564.
Molag, L. (2021). The local universality of Muttalib-Borodin ensembles when the parameter theta is the reciprocal of an integer. Nonlinearity, 34(5), 3485-3564. https://doi.org/10.1088/1361-6544/abeab6
Molag, L. (2021). The local universality of Muttalib-Borodin ensembles when the parameter theta is the reciprocal of an integer. Nonlinearity 34, 3485-3564.
Molag, L., 2021. The local universality of Muttalib-Borodin ensembles when the parameter theta is the reciprocal of an integer. Nonlinearity, 34(5), p 3485-3564.
L. Molag, “The local universality of Muttalib-Borodin ensembles when the parameter theta is the reciprocal of an integer”, Nonlinearity, vol. 34, 2021, pp. 3485-3564.
Molag, L.: The local universality of Muttalib-Borodin ensembles when the parameter theta is the reciprocal of an integer. Nonlinearity. 34, 3485-3564 (2021).
Molag, Leslie. “The local universality of Muttalib-Borodin ensembles when the parameter theta is the reciprocal of an integer”. Nonlinearity 34.5 (2021): 3485-3564.

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