117 citations · 646 across the 47 of their papers we have counts for
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Vertex operator solutions to the discrete KP-hierarchy
Mark Adler, Pierre van Moerbeke
Vertex operators, which are disguised Darboux maps, transform solutions of the KP equation into new ones. In this paper, we show that the bi-infinite sequence obtained by Darboux t…
The Pfaff lattice, Matrix integrals and a map from Toda to Pfaff
M. Adler, P. van Moerbeke
We study the Pfaff lattice, introduced by us in the context of a Lie algebra splitting of gl(infinity) into sp(infinity) and lower-triangular matrices. We establish a set of biline…
Integrals over classical Groups, Random permutations, Toda and Toeplitz lattices
Mark Adler, Pierre van Moerbeke
Matrix Fourier-like integrals over the classical groups O_+(n), O_-(n), Sp(n) and U(n) are connected with the distribution of the length of the longest increasing sequence in rando…
Pfaff tau-functions
M. Adler, T. Shiota, P. van Moerbeke
Consider the evolution $$ \frac{\pl m_\iy}{\pl t_n}=\Lb^n m_\iy, \frac{\pl m_\iy}{\pl s_n}=-m_\iy(\Lb^\top)^n, $$ on bi- or semi-infinite matrices $m_\iy=m_\iy(t,s)$, with skew-sym…
The spectrum of coupled random matrices
Mark Adler, Pierre van Moerbeke
The study of the spectrum of coupled random matrices has received rather little attention. To the best of our knowledge, coupled random matrices have been studied, to some extent,…
Classical skew orthogonal polynomials and random matrices
M. Adler, P. J. Forrester, T. Nagao +1
Skew orthogonal polynomials arise in the calculation of the -point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmet…
The Pfaff lattice and skew-orthogonal polynomials
M. Adler, E. Horozov, P. van Moerbeke
Consider a semi-infinite skew-symmetric moment matrix, $m_{\iy}$ evolving according to the vector fields $\pl m / \pl t_k=\Lb^k m+m \Lb^{\top k} ,$ where $\Lb$ is the shift matrix.…