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math.CO1999★ 19 cited
Random Words, Toeplitz Determinants and Integrable Systems. I
Alexander R. Its, Craig A. Tracy, Harold Widom
It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for t…
math-ph1999
Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
Pavel Bleher, Alexander Its
We derive semiclassical asymptotics for the orthogonal polynomials P_n(z) on the line with respect to the exponential weight \exp(-NV(z)), where V(z) is a double-well quartic polyn…