In noninteracting isolated quantum systems out of equilibrium, local subsystems typically
relax to nonthermal stationary states. In the standard framework, information on the rest of …

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 …

This paper reviews modern approaches to the construction of formal solutions to integrable
hierarchies of mathematical physics whose coefficients are answers to various enumerative …

We study a-deformation of monotone Hurwitz numbers, obtained by deforming Schur
functions into Jack symmetric functions. We give an evolution equation for this model and …

Double Hurwitz numbers enumerate branched covers of CP 1 with prescribed ramification
over two points and simple ramification elsewhere. In contrast to the single case, their …

Weingarten calculus is a completely general and explicit method to compute the moments of
the Haar measure on compact subgroups of matrix algebras. Particular cases of this …

Classical Hurwitz numbers count branched covers of the Riemann sphere with prescribed
ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle …

Going beyond the studies of single and double Hurwitz numbers, we report some progress
towards studying Hurwitz numbers which correspond to ramified coverings of the Riemann …

Hurwitz numbers count branched covers of the Riemann sphere with specified ramification,
or equivalently, transitive permutation factorizations in the symmetric group with specified …

In this paper, we prove a longstanding conjecture on the asymptotic behavior of a pair of
oscillatory matrix integrals: the Harish-Chandra/Itzykson-Zuber (HCIZ) integral, and the …