4 citations · 4 across the 2 of their papers we have counts for
5 papers
Asymptotics of the partition function of a random matrix model
Pavel Bleher, Alexander Its
We prove a number of results concerning the large asymptotics of the free energy of a random matrix model with a polynomial potential . Our approach is based on a deforma…
A Riemann-Hilbert Approach to the Akhiezer Polynomials
Y. Chen, A. Its
In this paper we study those polynomials orthogonal with respect to a particular weight over the union of disjoint intervals first introduced by N.I. Akhiezer, via a reformulation…
Double scaling limit in the random matrix model: the Riemann-Hilbert approach
Pavel Bleher, Alexander Its
We prove the existence of the double scaling limit in the unitary matrix model with quartic interaction, and we show that the correlation functions in the double scaling limit are…
The nonlinear steepest descent approach to the asymptotics of the second Painleve transcendent in the complex domain
A. R. Its, A. A. Kapaev
The asymptotics of the generic second Painleve transcendent in the complex domain is found and justified via the direct asymptotic analysis of the associated Riemann-Hilbert proble…
Random Words, Toeplitz Determinants and Integrable Systems. I
Alexander R. Its, Craig A. Tracy, Harold Widom
It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for t…