30 citations · 87 across the 9 of their papers we have counts for
10 papers
Mean-field avalanche size exponent for sandpiles on Galton-Watson trees
Antal Jarai, Wioletta M. Ruszel, Ellen Saada
We show that in abelian sandpiles on infinite Galton-Watson trees, the probability that the total avalanche has more than topplings decays as . We prove both quenched…
Geometry of the uniform spanning forest components in high dimensions
Martin T. Barlow, Antal A. Járai
In this note we study the geometry of the component of the origin in the Uniform Spanning Forest of , as well as in the Uniform Spanning Tree of wired subgraphs of $\…
Electrical resistance of the low dimensional critical branching random walk
Antal A. Járai, Asaf Nachmias
We show that the electrical resistance between the origin and generation n of the incipient infinite oriented branching random walk in dimensions d<6 is O(n^{1-alpha}) for some uni…
Cache optimized linear sieve
A. Járai, E. Vatai
Sieving is essential in different number theoretical algorithms. Sieving with large primes violates locality of memory access, thus degrading performance. Our suggestion on how to…
Minimal configurations and sandpile measures
Antal A. Jarai, Nicolas Werning
We give a new simple construction of the sandpile measure on an infinite graph G, under the sole assumption that each tree in the Wired Uniform Spanning Forest on G has one end alm…
Abelian sandpiles: an overview and results on certain transitive graphs
Antal A. Járai
We review the Majumdar-Dhar bijection between recurrent states of the Abelian sandpile model and spanning trees. We generalize earlier results of Athreya and Jarai on the infinite…
Rate of convergence estimates for the zero dissipation limit in Abelian sandpiles
Antal A. Járai
We consider a continuous height version of the Abelian sandpile model with small amount of bulk dissipation gamma > 0 on each toppling, in dimensions d = 2, 3. In the limit gamma -…
Approaching criticality via the zero dissipation limit in the abelian avalanche model
Antal A. Járai, Frank Redig, Ellen Saada
The discrete height abelian sandpile model was introduced by Bak, Tang & Wiesenfeld and Dhar as an example for the concept of self-organized criticality. When the model is modified…
Random walk on the incipient infinite cluster for oriented percolation in high dimensions
Martin T. Barlow, Antal A. Jarai, Takashi Kumagai +1
We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on . In dimensions , we obtain bounds on exit…
Infinite volume limit of the Abelian sandpile model in dimensions d >= 3
Antal A. Jarai, Frank Redig
We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume…