517 citations · 1k across the 29 of their papers we have counts for
30 papers
The Efron-Stein inequality for identically distributed pairs
Jnaneshwar Baslingker, Bálint Virág
We prove that the classical Efron--Stein inequality holds for independent exchangeable pairs \((X_i,Y_i)\). The same inequality fails for independent identically distributed pairs;…
Palm measures for Dirac operators and the Sine beta process
Benedek Valkó, Bálint Virág
We characterize the Palm measure of the Sine beta process as the eigenvalues of an associated operator with a specific boundary condition.
Large deviations for the interchange process on the interval and incompressible flows
Michał Kotowski, Bálint Virág
We use the framework of permuton processes to show that large deviations of the interchange process are controlled by the Dirichlet energy. This establishes a rigorous connection b…
RSK in last passage percolation: a unified approach
Duncan Dauvergne, Mihai Nica, Bálint Virág
We present a version of the RSK correspondence based on the Pitman transform and geometric considerations. This version unifies ordinary RSK, dual RSK and continuous RSK. We show t…
The scaling limit of the longest increasing subsequence
Duncan Dauvergne, Bálint Virág
We provide a framework for proving convergence to the directed landscape, the central object in the Kardar-Parisi-Zhang universality class. For last passage models, we show that co…
Three-halves variation of geodesics in the directed landscape
Duncan Dauvergne, Sourav Sarkar, Bálint Virág
We show that geodesics in the directed landscape have -variation and that weight functions along the geodesics have cubic variation. We show that the geodesic and its landscap…
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…
Brownian absolute continuity of the KPZ fixed point with arbitrary initial condition
Sourav Sarkar, Bálint Virág
We show that the law of the KPZ fixed point starting from arbitrary initial condition is absolutely continuous with respect to the law of Brownian motion on every compact inter…
Uniform convergence to the Airy line ensemble
Duncan Dauvergne, Mihai Nica, Bálint Virág
We show that classical integrable models of last passage percolation and the related nonintersecting random walks converge uniformly on compact sets to the Airy line ensemble. Our…
Uniform point variance bounds in classical beta ensembles
Joseph Najnudel, Bálint Virág
In this paper, we give bounds on the variance of the number of points of the circular and the Gaussian ensemble in arcs of the unit circle or intervals of the real line. These…
The bead process for beta ensembles
Joseph Najnudel, Bálint Virág
The bead process introduced by Boutillier is a countable interlacing of the determinantal sine-kernel point processes. We construct the bead process for general sine beta processes…
Bulk properties of the Airy line ensemble
Duncan Dauvergne, Bálint Virág
The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper is to provide a set of to…
The directed landscape
Duncan Dauvergne, Janosch Ortmann, Balint Virag
The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian las…
Entropy and expansion
Endre Csóka, Viktor Harangi, Bálint Virág
Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individ…
Circular support in random sorting networks
Duncan Dauvergne, Bálint Virág
A sorting network is a shortest path from to in the Cayley graph of the symmetric group generated by adjacent transpositions. For a uniform random sort…
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…
The Local Limit of Random Sorting Networks
Omer Angel, Duncan Dauvergne, Alexander E. Holroyd +1
A sorting network is a geodesic path from to in the Cayley graph of generated by adjacent transpositions. For a uniformly random sorting network,…
Spectral measures of factor of i.i.d. processes on vertex-transitive graphs
Ágnes Backhausz, Bálint Virág
We prove that a measure on is the spectral measure of a factor of i.i.d. process on a vertex-transitive infinite graph if and only if it is absolutely continuous with res…
Non-Liouville groups with return probability exponent at most 1/2
Michał Kotowski, Bálint Virág
We construct a finitely generated group without the Liouville property such that the return probability of a random walk satisfies . Re…
Independence ratio and random eigenvectors in transitive graphs
Viktor Harangi, Bálint Virág
A theorem of Hoffman gives an upper bound on the independence ratio of regular graphs in terms of the minimum of the spectrum of the adjacency matrix. To complement this…
The Liouville property for groups acting on rooted trees
Gideon Amir, Omer Angel, Nicolás Matte Bon +1
We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for e…
Random walks veering left
Raoul Normand, Bálint Virág
We study coupled random walks in the plane such that, at each step, the walks change direction by a uniform random angle plus an extra deterministic angle θ. We compute the Hausdor…
The Ginibre ensemble and Gaussian analytic functions
Manjunath Krishnapur, Bálint Virág
We show that as changes, the characteristic polynomial of the random matrix with i.i.d. complex Gaussian entries can be described recursively through a process anal…
Absolute continuity of the limiting eigenvalue distribution of the random Toeplitz matrix
Arnab Sen, Bálint Virág
We show that the limiting eigenvalue distribution of random symmetric Toeplitz matrices is absolutely continuous with density bounded by 8, partially answering a question of Bryc,…