There are a number of intriguing connections between Painlevé equations and orthogonal
polynomials, and this book is one of the first to provide an introduction to these. Researchers …

A bstract Generic Painlevé VI tau function τ (t) can be interpreted as four-point correlator of
primary fields of arbitrary dimensions in 2D CFT with c= 1. Using AGT combinatorial …

arxiv:1207.4990v3 [math.FA] 1 Dec 2012 Page 1 arxiv:1207.4990v3 [math.FA] 1 Dec 2012
Toeplitz matrices and Toeplitz determinants under the impetus of the Ising model. Some …

The goal of this article is to study how much the eigenvalues of large Hermitian random
matrices deviate from certain deterministic locations—or in other words, to investigate …

In this article we prove that suitable positive powers of the absolute value of the
characteristic polynomial of a Haar distributed random unitary matrix converge in law, as the …

We study asymptotic behavior for the determinants of n× n Toeplitz matrices corresponding
to symbols with two Fisher–Hartwig singularities at the distance 2 t≥ 0 from each other on …

A bstract Generic c= 1 four-point conformal blocks on the Riemann sphere can be seen as
the coefficients of Fourier expansion of the tau function of Painlevé VI equation with respect …

We obtain large $ N $ asymptotics for $ N\times N $ Hankel determinants corresponding to
non-negative symbols with Fisher-Hartwig (FH) singularities in the multi-cut regime. Our …

Topological phases protected by symmetry can occur in gapped and—surprisingly—in
critical systems. We consider non-interacting fermions in one dimension with spinless time …

We obtain an asymptotic formula for n * nn× n Toeplitz determinants as n → ∞ n→∞, for non-
negative symbols with any fixed number of Fisher–Hartwig singularities, which is uniform …