243 citations · 1.7k across the 42 of their papers we have counts for
42 papers
Actions in the Airy line ensemble and convergence to the Airy sheet
Balint Virag, Xuan Wu
Actions in the Airy line ensemble represent distances from an infinitely far object. We characterize the Airy sheet by S(x,.)=T^x(.,1), where T^x is the unique action in the Airy l…
The directed landscape seen from its trees
Mustazee Rahman, Balint Virag
A basic question about the directed landscape is how much of it can be reconstructed simply by knowing the shapes of its geodesics. We prove that the directed landscape can be reco…
KPZ fluctuations in the planar stochastic heat equation
Jeremy Quastel, Alejandro Ramirez, Balint Virag
We use a version of the Skorokhod integral to give a simple and rigorous formulation of the Wick-ordered (stochastic) heat equation with planar white noise, representing the free e…
Infinite geodesics, competition interfaces and the second class particle in the scaling limit
Mustazee Rahman, Balint Virag
We establish fundamental properties of infinite geodesics and competition interfaces in the directed landscape. We construct infinite geodesics in the directed landscape, establish…
Amenability of quadratic automaton groups
Gideon Amir, Omer Angel, Balint Virag
We give lower bounds for the electrical resistance between vertices in the Schreier graphs of the action of the linear (degree 1) and quadratic (degree 2) mother groups on the orbi…
The heat and the landscape I
Balint Virag
Heat flows in 1+1 dimensional stochastic environment converge after scaling to the random geometry described by the directed landscape. In this first part, we show that the O'Conne…
Operator limits of random matrices
Balint Virag
We present a brief introduction to the theory of operator limits of random matrices to non-experts. Several open problems and conjectures are given. Connections to statistics, inte…
Tracy-Widom fluctuations in 2D random Schrodinger operators
Marcin Kotowski, Bálint Virág
We construct a random Schrodinger operator on a subset of the hexagonal lattice and study its smallest positive eigenvalues. Using an asymptotic mapping, we relate them to the part…
Brownian motion as limit of the interchange process
Mustazee Rahman, Balint Virag
We prove that the random empirical measure of appropriately rescaled particle trajectories of the interchange process on path graphs converges weakly to the deterministic measure o…
Geometry of Permutation Limits
Mustazee Rahman, Balint Virag, Mate Vizer
This paper initiates a limit theory of permutation valued processes, building on the recent theory of permutons. We apply this to study the asymptotic behaviour of random sorting n…
Eigenvectors of the critical 1-dimensional random Schroedinger operator
Ben Rifkind, Balint Virag
The purpose of this paper is to understand in more detail the shape of the eigenvectors of the random Schroedinger operator H = Delta+V. Here Delta is the discrete Laplacian and V…
The Sine operator
Benedek Valkó, Bálint Virág
We show that Sine, the bulk limit of the Gaussian -ensembles is the spectrum of a self-adjoint random differential operator \[ f\to 2 {R_t^{-1}} \left[ \begin{array}{cc} 0 &…
Dyson's spike for random Schroedinger operators and Novikov-Shubin invariants of groups
Marcin Kotowski, Bálint Virág
We study Schroedinger operators with random edge weights and their expected spectral measures near zero. We prove that the measure exhibits a spike of the form $μ_H(-\varepsi…
Hölder continuity of the integrated density of states in the one-dimensional Anderson model
Eric Hart, Balint Virag
We consider the one-dimensional random Schrodinger operator H = H_0 + sigma V, where the potential V has i.i.d. entries with bounded support. We prove that the IDS is Holder contin…
A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes
Christian Sadel, Bálint Virág
We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix . Focusing on the eigenvalues of of a particu…
Local algorithms for independent sets are half-optimal
Mustazee Rahman, Balint Virag
We show that the largest density of factor of i.i.d. independent sets on the d-regular tree is asymptotically at most (log d)/d as d tends to infinity. This matches the lower bound…
Mean quantum percolation
Charles Bordenave, Arnab Sen, Balint Virag
We study the spectrum of adjacency matrices of random graphs. We develop two techniques to lower bound the mass of the continuous part of the spectral measure or the density of sta…
Universality of the Stochastic Airy Operator
Manjunath Krishnapur, Brian Rider, Balint Virag
We introduce a new method for studying universality of random matrices. Let T_n be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potentia…
Ramanujan graphings and correlation decay in local algorithms
Agnes Backhausz, Balazs Szegedy, Balint Virag
Let be a large-girth -regular graph and be a random process on the vertices of produced by a randomized local algorithm. We prove the upper bound $(k+1-2k/d)\Bigl(\f…
Invariant Gaussian processes and independent sets on regular graphs of large girth
Endre Csóka, Balázs Gerencsér, Viktor Harangi +1
We prove that every 3-regular, n-vertex simple graph with sufficiently large girth contains an independent set of size at least 0.4361n. (The best known bound is 0.4352n.) In fact,…
Speed exponents of random walks on groups
Gideon Amir, Balint Virag
For every 3/4 <= beta < 1 we construct a finitely generated group so that the expected distance of the simple random walk from its starting point is within a constant factor of n^b…
Kesten's theorem for Invariant Random Subgroups
Miklos Abert, Yair Glasner, Balint Virag
An invariant random subgroup of the countable group Γ is a random subgroup of Γ whose distribution is invariant under conjugation by all elements of Γ. We prove that for a nonamena…
The measurable Kesten theorem
Miklos Abert, Yair Glasner, Balint Virag
We give explicit estimates between the spectral radius and the densities of short cycles for finite d-regular graphs. This allows us to show that the essential girth of a finite d-…
The scaling limit of the critical one-dimensional random Schrodinger operator
Evgenij Kritchevski, Benedek Valko, Balint Virag
We consider two models of one-dimensional discrete random Schrodinger operators (H_n ψ)_l =ψ_{l-1}+ψ_{l +1}+v_l ψ_l, ψ_0=ψ_{n+1}=0 in the cases v_k=σω_k/\sqrt{n} and v_k=σω_k/ \sqr…