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math.CA2002★ 1 cited
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…
math.CA1999
A Fredholm determinant formula for Toeplitz determinants
Alexei Borodin, Andrei Okounkov
We prove a formula expressing a general n by n Toeplitz determinant as a Fredholm determinant of an operator 1-K acting on l_2({n,n+1,...}), where the kernel K admits an integral r…