117 citations · 646 across the 47 of their papers we have counts for
14 papers · 1 filter
Transversal Cusp-Airy versus Cusp-Airy for Lozenge Tilings
Mark Adler, Pierre van Moerbeke
The fluctuations of lozenge tilings of hexagons with one or several cuts (nonconvexities) along opposite sides are governed by the (discrete-continuous) tacnode kernel ${\mathbb L}…
Double Interlacing in Random Tiling Models
Mark Adler, Pierre van Moerbeke
Random tilings of very large domains will typically lead to a solid, a liquid, and a gas phase. In the two-phase case, the solid-liquid boundary (arctic curve) is smooth, possibly…
A singular Toeplitz determinant and the discrete tacnode kernel for skew-Aztec Rectangles
Mark Adler, Kurt Johansson, Pierre van Moerbeke
Random tilings of geometrical shapes with dominos or lozenges have been a rich source of universal statistical distributions. This paper deals with domino tilings of checker board…
The AKS Theorem, A.C.I. Systems and Random Matrix Theory
Mark Adler, Pierre van Moerbeke
This paper gives the most general form of the Adler-Kostant-Symes Theorem, and many applications of it, both finite and infinite dimensional, the former yielding algebraic complete…
Probability distributions related to tilings of non-convex Polygons
Mark Adler, Pierre van Moerbeke
This paper is based on the study of random lozenge tilings of non-convex polygonal regions with interacting non-convexities (cuts) and the corresponding asymptotic kernel as in [3]…
Lozenge tilings of hexagons with cuts and asymptotic fluctuations: a new universality class
Mark Adler, Kurt Johansson, Pierre van Moerbeke
This paper investigates lozenge tilings of non-convex hexagonal regions and more specifically the asymptotic fluctuations of the tilings within and near the strip formed by opposit…
Tilings of non-convex Polygons, skew-Young Tableaux and determinantal Processes
Mark Adler, Kurt Johansson, Pierre van Moerbeke
This paper studies random lozenge tilings of general non-convex polygonal regions. We show that the pairwise interaction of the non-convexities leads asymptotically to new kernels…
Nonlinear PDEs for Fredholm determinants arising from string equations
M. Adler, M. Cafasso, P. van Moerbeke
String equations related to 2D gravity seem to provide, quite naturally and systematically, integrable kernels, in the sense of Its-Izergin-Korepin and Slavnov. Some of these kerne…
Nonlinear PDEs for gap probabilities in random matrices and KP theory
M. Adler, M. Cafasso, P. van Moerbeke
Airy and Pearcey-like kernels and generalizations arising in random matrix theory are expressed as double integrals of ratios of exponentials, possibly multiplied with a rational f…
Nonintersecting random walks in the neighborhood of a symmetric tacnode
Mark Adler, Patrik L. Ferrari, Pierre van Moerbeke
Consider a continuous time random walk in with independent and exponentially distributed jumps . The model in this paper consists in an infinite number of such r…
Moment matrices and multi-component KP, with applications to random matrix theory
Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
Questions on random matrices and on non-intersecting Brownian motions have led to the study of moment matrices with regard to several weights. The purpose of this paper is to show…
Singularity confinement for a class of -th order difference equations of combinatorics
M. Adler, P. van Moerbeke, P. Vanhaecke
In a recent publication, it was shown that a large class of integrals over the unitary group U(n) satisfy difference equations over , involving a finite number of steps; special…
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…
Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum
Mark Adler, Pierre van Moerbeke
Given the Hermitian, symmetric and symplectic ensembles, it is shown that the probability that the spectrum belongs to one or several intervals satisfies a nonlinear PDE. This is d…