9 citations · 10 across the 3 of their papers we have counts for
11 papers
Averages of Characteristic Polynomials in Random Matrix Theory
A. Borodin, E. Strahov
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determi…
Janossy Densities I. Determinantal Ensembles
Alexei Borodin, Alexander Soshnikov
We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for beta=2 polynomial ensembles of…
Isomonodromy transformations of linear systems of difference equations
Alexei Borodin
We introduce and study isomonodromy transformations of the matrix linear difference equation Y(z+1)=A(z)Y(z) with polynomial (or rational) A(z). Our main result is a construction o…
Discrete gap probabilities and discrete Painleve equations
Alexei Borodin
We prove that Fredholm determinants of the form det(1-K_s), where K_s is the restriction of either the discrete Bessel kernel or the discrete {}_2F_1 kernel to {s,s+1,...}, can be…
Fredholm determinants, Jimbo-Miwa-Ueno tau-functions, and representation theory
Alexei Borodin, Percy Deift
The authors show that a wide class of Fredholm determinants arising in the representation theory of "big" groups such as the infinite-dimensional unitary group, solve Painleve equa…
Asymptotic representation theory and Riemann-Hilbert problem
Alexei Borodin
We show how the Riemann-Hilbert problem can be used to compute correlation kernels for determinantal point processes arising in different models of asymptotic combinatorics and rep…