63 citations · 195 across the 11 of their papers we have counts for
13 papers · 1 filter
Operator level limit of the circular Jacobi -ensemble
Yun Li, Benedek Valkó
We prove an operator level limit for the circular Jacobi -ensemble. As a result, we characterize the counting function of the limit point process via coupled systems of stochast…
The many faces of the stochastic zeta function
Benedek Valkó, Bálint Virág
We introduce a framework to study the random entire function whose zeros are given by the Sine process, the bulk limit of beta ensembles. We present several equivalent ch…
Operator level hard-to-soft transition for -ensembles
Laure Dumaz, Yun Li, Benedek Valkó
The soft and hard edge scaling limits of -ensembles can be characterized as the spectra of certain random Sturm-Liouville operators. It has been shown that by tuning the paramet…
Random walk on the randomly-oriented Manhattan lattice
Sean Ledger, Bálint Tóth, Benedek Valkó
In the randomly-oriented Manhattan lattice, every line in is assigned a uniform random direction. We consider the directed graph whose vertex set is a…
Operator limit of the circular beta ensemble
Benedek Valkó, Bálint Virág
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 oper…
Overcrowding asymptotics for the Sine_beta process
Diane Holcomb, Benedek Valkó
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 at least n points in a…
Fluctuation exponents for directed polymers in the intermediate disorder regime
Gregorio R. Moreno Flores, Timo Seppäläinen, Benedek Valkó
We compute the fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate regime. This regime corresponds to taking t…
Large deviations for the Sine_beta and Sch_tau processes
Diane Holcomb, Benedek Valkó
We study two one-parameter families of point processes connected to random matrices: the Sine_beta and Sch_tau processes. The first one is the bulk point process limit for the Gaus…
Bounds for scaling exponents for a 1+1 dimensional directed polymer in a Brownian environment
Timo Seppäläinen, Benedek Valkó
We study the scaling exponents of a 1+1-dimensional directed polymer in a Brownian random environment introduced by O'Connell and Yor. For a version of the model with boundary cond…
Bulk scaling limit of the Laguerre ensemble
Stéphanie Jacquot, Benedek Valkó
We consider the beta-Laguerre ensemble, a family of distributions generalizing the joint eigenvalue distribution of the Wishart random matrices. We show that the bulk scaling limit…
Diffusivity bounds for 1D Brownian polymers
Pierre Tarrès, Bálint Tóth, Benedek Valkó
We study the asymptotic behavior of a self-interacting one-dimensional Brownian polymer first introduced by Durrett and Rogers [Probab. Theory Related Fields 92 (1992) 337--349]. T…
The TASEP speed process
Gideon Amir, Omer Angel, Benedek Valkó
In the multi-type totally asymmetric simple exclusion process (TASEP) on the line, each site of Z is occupied by a particle labeled with some number, and two neighboring particles…
Large gaps between random eigenvalues
Benedek Valkó, Bálint Virág
We show that in the point process limit of the bulk eigenvalues of -ensembles of random matrices, the probability of having no eigenvalue in a fixed interval of size is give…