Monotone Hurwitz Numbers and the HCIZ Integral

I. P. Goulden[1]; Mathieu Guay-Paquet[2]; Jonathan Novak[3]

  • [1] Department of Combinatorics & Optimization University of Waterloo 200 University Avenue West Waterloo, ON N2L 3G1 Canada
  • [2] LaCIM Université du Québec à Montréal 201 Avenue du Président-Kennedy Montréal, QC H2X 3Y7 Canada
  • [3] Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave. Boston, MA 02114 USA

Annales mathématiques Blaise Pascal (2014)

  • Volume: 21, Issue: 1, page 71-89
  • ISSN: 1259-1734

Abstract

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In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of z = 0 . Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.

How to cite

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Goulden, I. P., Guay-Paquet, Mathieu, and Novak, Jonathan. "Monotone Hurwitz Numbers and the HCIZ Integral." Annales mathématiques Blaise Pascal 21.1 (2014): 71-89. <http://eudml.org/doc/275580>.

@article{Goulden2014,
abstract = {In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of $z=0$. Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.},
affiliation = {Department of Combinatorics & Optimization University of Waterloo 200 University Avenue West Waterloo, ON N2L 3G1 Canada; LaCIM Université du Québec à Montréal 201 Avenue du Président-Kennedy Montréal, QC H2X 3Y7 Canada; Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave. Boston, MA 02114 USA},
author = {Goulden, I. P., Guay-Paquet, Mathieu, Novak, Jonathan},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Matrix models; Hurwitz numbers; asymptotic analysis; matrix models},
language = {eng},
month = {1},
number = {1},
pages = {71-89},
publisher = {Annales mathématiques Blaise Pascal},
title = {Monotone Hurwitz Numbers and the HCIZ Integral},
url = {http://eudml.org/doc/275580},
volume = {21},
year = {2014},
}

TY - JOUR
AU - Goulden, I. P.
AU - Guay-Paquet, Mathieu
AU - Novak, Jonathan
TI - Monotone Hurwitz Numbers and the HCIZ Integral
JO - Annales mathématiques Blaise Pascal
DA - 2014/1//
PB - Annales mathématiques Blaise Pascal
VL - 21
IS - 1
SP - 71
EP - 89
AB - In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of $z=0$. Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.
LA - eng
KW - Matrix models; Hurwitz numbers; asymptotic analysis; matrix models
UR - http://eudml.org/doc/275580
ER -

References

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