A. J'arai

activity

20072026

most citedAnchored burning bijections on finite and infinite graphs

4 citations · 5 across the 10 of their papers we have counts for

collaborators

13 papers

math.PR2026

Scaling and partial universality of the height zero probability in the 2D Abelian sandpile

Miles W. Elvidge, Antal A. Járai

We study the extent of universality in the scaling of the height $0$ probability of the stationary Abelian sandpile on lattice approximations of a region $U \subset C$ wit…

math.PR2021

Interlacement limit of a stopped random walk trace on a torus

Antal A. Járai, Minwei Sun

We consider a simple random walk on $Z^{d}$ started at the origin and stopped on its first exit time from $(- L, L)^{d} \cap Z^{d}$ . Write $L$ in the form $L = m N$ with…

math.PR2020

Logarithmic correction to resistance

Antal A. Járai, Dante Mata López

We study the trace of the incipient infinite oriented branching random walk in $Z^{d} \times Z_{+}$ when the dimension is $d = 6$ . Under suitable moment assumptions,…

math.PR2020

On the tail of the branching random walk local time

Omer Angel, Tom Hutchcroft, Antal A. Járai

Consider a critical branching random walk on $Z^{d}$ , $d \geq 1$ , started with a single particle at the origin, and let $L (x)$ be the total number of particles that ever visi…

math.PR2019★ 1 cited

Edgeworth expansion with error estimates for power law shot noise

Antal A. Járai

Consider a homogeneous Poisson process in $R^{d}$ , $d \geq 1$ . Let $R_{1} < R_{2} < \dots$ be the distances of the points from the origin, and let $S = R_1^{-γ} + R_2^{-γ} + \dot…

math.PR2019

Asymptotics of the optimum in discrete sequential assignment

Antal A. Járai

We consider the stochastic sequential assignment problem of Derman, Lieberman and Ross (1972) corresponding to a discrete distribution supported on a finite set of points. We use l…

math.PR2019

Asymptotic height distribution in high-dimensional sandpiles

Antal A Járai, Minwei Sun

We give an asymptotic formula for the single site height distribution of Abelian sandpiles on $Z^{d}$ as $d \to \infty$ , in terms of $Poisson (1)$ probabilities. We…

math.PR2016

Inequalities for critical exponents in $d$ -dimensional sandpiles

Sandeep Bhupatiraju, Jack Hanson, Antal A. Járai

Consider the Abelian sandpile measure on $Z^{d}$ , $d \geq 2$ , obtained as the $L \to \infty$ limit of the stationary distribution of the sandpile on $[-L,L]^d \cap \mathbb{Z}…

math.PR2015

Phase transition in a sequential assignment problem on graphs

Antal A. Járai

We study the following game on a finite graph $G = (V, E)$ . At the start, each edge is assigned an integer $n_{e} \geq 0$ , $n = \sum_{e \in E} n_{e}$ . In round $t$ , $1 \leq t \leq n$ , a u…

math.PR2014★ 4 cited

Anchored burning bijections on finite and infinite graphs

Samuel L. Gamlin, Antal A. Járai

Let $G$ be an infinite graph such that each tree in the wired uniform spanning forest on $G$ has one end almost surely. On such graphs $G$ , we give a family of continuous, measure…

math.PR2014

Sandpile models

Antal A. Járai

This survey is an extended version of lectures given at the Cornell Probability Summer School 2013. The fundamental facts about the Abelian sandpile model on a finite graph and its…

math.PR2007

The size of a pond in 2D invasion percolation

Jacob van den Berg, Antal A. Járai, Bálint Vágvölgyi

We consider invasion percolation on the square lattice. It has been proved by van den Berg, Peres, Sidoravicius and Vares, that the probability that the radius of a so-called pond…

math.PR2007

Ladder Sandpiles

Antal A. Járai, Russell Lyons

We study Abelian sandpiles on graphs of the form $G \times I$ , where $G$ is an arbitrary finite connected graph, and $I \subset Z$ is a finite interval. We show that for any fixed…

Scaling and partial universality of the height zero probability in the 2D Abelian sandpile

Interlacement limit of a stopped random walk trace on a torus

Logarithmic correction to resistance

On the tail of the branching random walk local time

Edgeworth expansion with error estimates for power law shot noise

Asymptotics of the optimum in discrete sequential assignment

Asymptotic height distribution in high-dimensional sandpiles

Inequalities for critical exponents in d-dimensional sandpiles

Phase transition in a sequential assignment problem on graphs

Anchored burning bijections on finite and infinite graphs

Sandpile models

The size of a pond in 2D invasion percolation

Ladder Sandpiles

Inequalities for critical exponents in $d$ -dimensional sandpiles