High-dimensional graphical networks of (2007)
Mark Holmes, Antal A. Járai, Akira Sakai, Gordon Slade
self-avoiding walks
The size of a pond in 2D invasion percolation (2007)
Berg, Jacob Van Den, Járai, Antal A., Vágvölgyi, Bálint
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 is larger than n,...
Járai, Antal A., Lyons, Russell
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 $G$ with at least...
Incipient infinite percolation clusters in 2D (2003)
We study several kinds of large critical percolation clusters in two dimensions. We show that from the microscopic (lattice scale) perspective these clusters can be described by Kesten's incipient...
Abelian sandpile models (2003)
Siva R. Athreya, Antal A. Járai
Infinite volume limit for the stationary distribution of