106 citations · 142 across the 7 of their papers we have counts for
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math-ph2001
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…
math-ph2001
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…