278 citations · 1.7k across the 68 of their papers we have counts for
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Asymptotics of the instantons of Painleve I
Stavros Garoufalidis, Alexander Its, Andrei Kapaev +1
The 0-instanton solution of Painlevé I is a sequence of complex numbers which appears universally in many enumerative problems in algebraic geometry, graph theory, matr…
Asymptotics for a special solution of the thirty fourth Painleve equation
A. R. Its, A. B. J. Kuijlaars, J. Ostensson
In a previous paper we studied the double scaling limit of unitary random matrix ensembles of the form Z_{n,N}^{-1} |\det M|^{2α} e^{-N \Tr V(M)} dM with α> -1/2. The factor |\det…
Total integrals of global solutions to Painleve II
Jinho Baik, Robert Buckingham, Jeffery DiFranco +1
We evaluate the total integral from negative infinity to positive infinity of all global solutions to the Painleve II equation on the real line. The method is based on the interpla…
Painléve III and a singular linear statistics in Hermitian random matrix ensembles I
Yang Chen, Alexander Its
In this paper, we study a certain linear statistics of the unitary Laguerre ensembles, motivated in part by an integrable quantum field theory at finite temperature. It transpires…
Normal matrix models, dbar-problem, and orthogonal polynomials on the complex plane
Alexander R. Its, Leon A. Takhtajan
We introduce a dbar-formulation of the orthogonal polynomials on the complex plane, and hence of the related normal matrix model, which is expected to play the same role as the Rie…
Critical edge behavior in unitary random matrix ensembles and the thirty fourth Painleve transcendent
A. R. Its, A. B. J. Kuijlaars, J. Ostensson
We describe a new universality class for unitary invariant random matrix ensembles. It arises in the double scaling limit of ensembles of random Hermitian matrices $Z_…