37 citations · 83 across the 9 of their papers we have counts for
13 papers
Limit Theorems Under Several Linear Constraints
Fabrice Gamboa, Martin Venker
We study real-valued random variables subject to several linear constraints. Our main result is a weighted Central Limit Theorem, determining which linear combinations of these…
Transition Analysis: From the Airy and Pearcey Kernels to the Sine Kernel
Thorsten Neuschel, Martin Venker
We study transitions between the three universal limiting kernels Airy, Pearcey and sine kernel, arising in Random Matrix Theory at edge, cusp and bulk points of the spectrum. Unde…
Boundary Asymptotics of Non-Intersecting Brownian Motions: Pearcey, Airy and a Transition
Thorsten Neuschel, Martin Venker
We study non-intersecting Brownian motions, corresponding to the eigenvalues of an Hermitian Brownian motion. At the boundary of their limit shape we find that only…
Critical Behavior of Non-Intersecting Brownian Motions
Tom Claeys, Thorsten Neuschel, Martin Venker
We study non-intersecting Brownian motions corresponding to initial configurations which have a vanishing density in the large limit at an interior point of the support. It…
Random Moment Problems under Constraints
Holger Dette, Dominik Tomecki, Martin Venker
We investigate moment sequences of probability measures on under constraints of certain moments being fixed. This corresponds to studying sections of -th mo…
Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices
Tom Claeys, Thorsten Neuschel, Martin Venker
We explore the boundaries of sine kernel universality for the eigenvalues of Gaussian perturbations of large deterministic Hermitian matrices. Equivalently, we study for determinis…
Universality in Random Moment Problems
Holger Dette, Dominik Tomecki, Martin Venker
Let denote the set of vectors of the first moments of probability measures on with existing moments. The investigation of such moment sp…
Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble
Gernot Akemann, Milan Cikovic, Martin Venker
We consider non-Gaussian extensions of the elliptic Ginibre ensemble of complex non-Hermitian random matrices by fixing the trace of the matrix with a…
Empirical Spacings of Unfolded Eigenvalues
Kristina Schubert, Martin Venker
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of po…
Edge Statistics for a Class of Repulsive Particle Systems
Thomas Kriecherbauer, Martin Venker
We study a class of interacting particle systems on which was recently investigated by F. Götze and the second author [GV14]. These ensembles generalize eigenvalue ens…
Global Asymptotics for the Christoffel-Darboux Kernel of Random Matrix Theory
Thomas Kriecherbauer, Kristina Schubert, Katharina Schüler +1
The investigation of universality questions for local eigenvalue statistics continues to be a driving force in the theory of Random Matrices. For Matrix Models [53] the method of o…
Particle Systems with Repulsion Exponent and Random Matrices
Martin Venker
We consider a class of particle systems generalizing the -Ensembles from random matrix theory. In these new ensembles, particles experience repulsion of power when getting…
Local universality of repulsive particle systems and random matrices
Friedrich Götze, Martin Venker
We study local correlations of certain interacting particle systems on the real line which show repulsion similar to eigenvalues of random Hermitian matrices. Although the new part…