9 citations · 10 across the 3 of their papers we have counts for
4 papers · 1 filter
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…
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…