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pro vyhledávání: '"Venker, Martin"'
Autor:
Neuschel, Thorsten, Venker, Martin
We study $n$ non-intersecting Brownian motions, corresponding to the eigenvalues of an $n\times n$ Hermitian Brownian motion. At the boundary of their limit shape we find that only three universal processes can arise: the Pearcey process close to mer
Externí odkaz:
http://arxiv.org/abs/2212.03816
Publikováno v:
Commun. Math. Phys. 378, no. 2 (2020) 1501-1537
We study $n$ non-intersecting Brownian motions corresponding to initial configurations which have a vanishing density in the large $n$ limit at an interior point of the support. It is understood that the point of vanishing can propagate up to a criti
Externí odkaz:
http://arxiv.org/abs/1912.02142
Publikováno v:
Ann. Probab. 48, no. 2 (2020) 672-713
We investigate moment sequences of probability measures on $E\subset\mathbb{R}$ under constraints of certain moments being fixed. This corresponds to studying sections of $n$-th moment spaces, i.e. the spaces of moment sequences of order $n$. By equi
Externí odkaz:
http://arxiv.org/abs/1806.04652
Publikováno v:
Random Matrices Theory Appl. 8, no. 3, 50 pp., 2019
We explore the boundaries of sine kernel universality for the eigenvalues of Gaussian perturbations of large deterministic Hermitian matrices. Equivalently, we study for deterministic initial data the time after which Dyson's Brownian motion exhibits
Externí odkaz:
http://arxiv.org/abs/1712.08432
Publikováno v:
Electron. J. Probab. 23, no. 15, pp. 1-23, 2018
Let $\mathcal{M}_n(E)$ denote the set of vectors of the first $n$ moments of probability measures on $E\subset\mathbb{R}$ with existing moments. The investigation of such moment spaces in high dimension has found considerable interest in the recent l
Externí odkaz:
http://arxiv.org/abs/1709.02266
Publikováno v:
The Annals of Probability, 2020 Mar 01. 48(2), 672-713.
Externí odkaz:
https://www.jstor.org/stable/26922929
Publikováno v:
Commun. Math. Phys. 362 no. 3 (2018) 1111-1141
We consider non-Gaussian extensions of the elliptic Ginibre ensemble of complex non-Hermitian random matrices by fixing the trace $\operatorname{Tr}(XX^*)$ of the matrix $X$ with a hard or soft constraint. These ensembles have correlated matrix entri
Externí odkaz:
http://arxiv.org/abs/1610.06517
Autor:
Schubert, Kristina, Venker, Martin
Publikováno v:
Electron. J. Probab. 20, no. 120, pp. 1-37, 2015
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 points tends to infinity, we prove convergence of the empirical distribu
Externí odkaz:
http://arxiv.org/abs/1505.07664
Autor:
Kriecherbauer, Thomas, Venker, Martin
Publikováno v:
Probab. Theory Relat. Fields 170, pp. 617-655, 2018
We study a class of interacting particle systems on $\mathbb{R}$ which was recently investigated by F. G\"otze and the second author [GV14]. These ensembles generalize eigenvalue ensembles of Hermitian random matrices by allowing different interactio
Externí odkaz:
http://arxiv.org/abs/1501.07501
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