Zobrazeno 1 - 10
of 107
pro vyhledávání: '"Valkó, Benedek"'
Autor:
Li, Yun, Valkó, Benedek
We study the scaling limit of the rank-one truncation of various beta ensemble generalizations of classical unitary/orthogonal random matrices: the circular beta ensemble, the real orthogonal beta ensemble, and the circular Jacobi beta ensemble. We d
Externí odkaz:
http://arxiv.org/abs/2310.14995
Autor:
Holcomb, Diane, Valkó, Benedek
We give overcrowding estimates for the Sine(beta) process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having exactly n points in a fixed interval is given by e(-beta/2n2) log(n)+O(n(2)) as n -> infinit
Externí odkaz:
http://hdl.handle.net/10150/625509
http://arizona.openrepository.com/arizona/handle/10150/625509
http://arizona.openrepository.com/arizona/handle/10150/625509
Autor:
Valkó, Benedek, Virág, Bálint
Publikováno v:
Stochastic Processes and their Applications, Volume 163, September 2023, Pages 106-135
We characterize the Palm measure of the Sine beta process as the eigenvalues of an associated operator with a specific boundary condition.
Comment: 33 pages, no figures
Comment: 33 pages, no figures
Externí odkaz:
http://arxiv.org/abs/2207.10626
Autor:
Li, Yun, Valkó, Benedek
We prove an operator level limit for the circular Jacobi $\beta$-ensemble. As a result, we characterize the counting function of the limit point process via coupled systems of stochastic differential equations. We also show that the normalized charac
Externí odkaz:
http://arxiv.org/abs/2108.11039
We study a model for the entanglement of a two-dimensional reflecting Brownian motion in a bounded region divided into two halves by a wall with three or more small windows. We map the Brownian motion into a Markov Chain on the fundamental groupoid o
Externí odkaz:
http://arxiv.org/abs/2010.08524
Autor:
Valkó, Benedek, Virág, Bálint
Publikováno v:
Geometric and Functional Analysis 32, no. 5 (2022): 1160-1231
We introduce a framework to study the random entire function $\zeta_\beta$ whose zeros are given by the Sine$_\beta$ process, the bulk limit of beta ensembles. We present several equivalent characterizations, including an explicit power series repres
Externí odkaz:
http://arxiv.org/abs/2009.04670
The soft and hard edge scaling limits of $\beta$-ensembles can be characterized as the spectra of certain random Sturm-Liouville operators. It has been shown that by tuning the parameter of the hard edge process one can obtain the soft edge process a
Externí odkaz:
http://arxiv.org/abs/2003.02779
Autor:
Valkó, Benedek, Virág, Bálint
Publikováno v:
In Stochastic Processes and their Applications September 2023 163:106-135
In the randomly-oriented Manhattan lattice, every line in $\mathbb{Z}^d$ is assigned a uniform random direction. We consider the directed graph whose vertex set is $\mathbb{Z}^d$ and whose edges connect nearest neighbours, but only in the direction f
Externí odkaz:
http://arxiv.org/abs/1802.01558
Autor:
Valkó, Benedek, Virág, Bálint
Publikováno v:
Annals of Probability 2020, Vol. 48, No. 3, 1286-1316
We provide a precise coupling of the finite circular beta ensembles and their limit process via their operator representations. We prove explicit bounds on the distance of the operators and the corresponding point processes. We also prove an estimate
Externí odkaz:
http://arxiv.org/abs/1710.06988