63 citations · 66 across the 4 of their papers we have counts for
13 papers
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…
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…
Rational solutions to the Pfaff lattice and Jack polynomials
Mark Adler, Vadim B. Kuznetsov, Pierre van Moerbeke
The finite Pfaff lattice is given by commuting Lax pairs involving a finite matrix L (zero above the first subdiagonal) and a projection onto Sp(N). The lattice admits solutions su…
Recursion relations for Unitary integrals, Combinatorics and the Toeplitz Lattice
Mark Adler Pierre van Moerbeke
The Toeplitz determinants (of increasing size) associated with the symbols or satisfy recursion relations, thus expressing all the T…
Integrals over Grassmannians and Random permutations
M. Adler, P. van Moerbeke
In testing the independence of two Gaussian populations, one computes the distribution of the sample canonical correlation coefficients, given that the actual correlation is zero.…
Integrable Lattices: Random Matrices and Random Permutations
Pierre van Moerbeke
These lectures present a survey of recent developments in the area of random matrices (finite and infinite) and random permutations. These probabilistic problems suggest matrix int…