117 citations · 646 across the 47 of their papers we have counts for
16 papers · 1 filter
Coupled GUE-minor Processes
Mark Adler, Pierre van Moerbeke
This paper deals with two GUE-matrices, coupled together through some inequalities between the spectra of the first few (small) principal minors. The main results of the paper is t…
Tacnode GUE-minor Processes and Double Aztec Diamonds
Mark Adler, Sunil Chhita, Kurt Johansson +1
We study random domino tilings of a Double Aztec diamond, a region consisting of two overlapping Aztec diamonds. The random tilings give rise to two discrete determinantal point pr…
Random matrix minor processes related to percolation theory
Mark Adler, Pierre van Moerbeke, Dong Wang
This paper studies a number of matrix models of size n and the associated Markov chains for the eigenvalues of the models for consecutive n's. They are consecutive principal minors…
Double Aztec Diamonds and the Tacnode Process
Mark Adler, Kurt Johansson, Pierre van Moerbeke
Discrete and continuous non-intersecting random processes have given rise to critical "infinite dimensional diffusions", like the Airy process, the Pearcey process and variations t…
From the Pearcey to the Airy process
Mark Adler, Mattia Cafasso, Pierre van Moerbeke
Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scalin…
Consecutive Minors for Dyson's Brownian Motions
Mark Adler, Eric Nordenstam, Pierre van Moerbeke
In 1962, Dyson introduced dynamics in random matrix models, in particular into GUE (also for beta=1 and 4), by letting the entries evolve according to independent Ornstein-Uhlenbec…
The Dyson Brownian minor process
Mark Adler, Eric Nordenstam, Pierre van Moerbeke
Consider an Hermitean matrix valued stochastic process where the matrix elements evolve according to Ornstein-Uhlenbeck processes. It is well known…
Non-intersecting Brownian motions leaving from and going to several points
Mark Adler, Pierre van Moerbeke, Didier Vanderstichelen
Consider n non-intersecting Brownian motions on , depending on time , with particles forced to leave from at time , , and $…
A PDE for Nonintersecting Brownian Motions and Applications
Mark Adler, Jonathan Delepine, Pierre van Moerbeke +1
Consider non-intersecting Brownian motions on the real line, starting from the origin at t=0, with a number of particles forced to reach p distinct target points at time t=1. This…
Universality of the Pearcey process
Mark Adler, Nicolas Orantin, Pierre van Moerbeke
Consider non-intersecting Brownian motions on the line leaving from the origin and forced to two arbitrary points. Letting the number of Brownian particles tend to infinity, and up…
Airy processes with wanderers and new universality classes
Mark Adler, Patrik L. Ferrari, Pierre van Moerbeke
Consider nonintersecting Brownian bridges, with of them leaving from 0 at time and returning to 0 at time , while the remaining ones (wanderers) go from $…
Dyson's non-intersecting Brownian motions with a few outliers
Mark Adler, Jonathan Delepine, Pierre van Moerbeke
Consider n non-intersecting particles on the real line (Dyson Brownian motions), all starting from the origin at time=0, and forced to return to x=0 at time=1. For large n, the ave…
PDE's for the Gaussian ensemble with external source and the Pearcey distribution
Mark Adler, Pierre van Moerbeke
The present paper studies a Gaussian Hermitian random matrix ensemble with external source, given by a fixed diagonal matrix with two eigenvalues a and -a. As a first result, the p…
Expectations of hook products on large partitions
Mark Adler, Alexei Borodin, Pierre van Moerbeke
Given uniform probability on words of length M=Np+k, from an alphabet of size p, consider the probability that a word (i) contains a subsequence of letters (p, p-1,...,1) in that o…
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…