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math.PR2004★ 63 cited
PDEs for the joint distributions of the Dyson, Airy and Sine processes
Mark Adler, Pierre van Moerbeke
In a celebrated paper, Dyson shows that the spectrum of an n\times n random Hermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as n noncolliding Browni…
math.PR2003★ 1 cited
Virasoro action on Schur function expansions, skew Young tableaux and random walks
M. Adler, P. van Moerbeke
It is known that some matrix integrals over U(n) satisfy an sl(2,R)-algebra of Virasoro constraints. Acting with these Virasoro generators on 2-dimensional Schur function expansion…