One-dimensional long-range diffusion-limited aggregation III -- The limit aggregate (2009)
In this paper we study the structure of the limit aggregate (the union of all finite-time aggregates) of the one-dimensional long range diffusion limited aggregation process defined in...
One-dimensional long-range diffusion-limited aggregation I (2009)
Amir, Gideon, Angel, Omer, Benjamini, Itai, Kozma, Gady
We examine diffusion-limited aggregation generated by a random walk on Z with long jumps. We derive upper and lower bounds on the growth rate of the aggregate as a function of the number moments a...
On Fixation of Activated Random Walks (2009)
Amir, Gideon, Gurel-Gurevich, Ori
We prove that for the Activated Random Walks model on transitive unimodular graphs, if there is fixation, then every particle eventually fixates, almost surely. We deduce that the critical density is...
Amenability of linear-activity automaton groups (2009)
Amir, Gideon, Angel, Omer, Virag, Balint
We prove that every linear-activity automaton group is amenable. The proof is based on showing that a sufficiently symmetric random walk on a specially constructed degree 1 automaton group -- the...
The TASEP speed process (2008)
Amir, Gideon, Angel, Omer, Valko, Benedek
In a multi-type totally asymmetric simple exclusion process (TASEP) on the line, each site of Z is occupied by a particle labeled with a number and two neighboring particles are interchanged at rate...
A special set of exceptional times for dynamical random walk on Z2 (2008)
Amir, Gideon; University Of Toronto; Gidi.amir@gmail.com, Hoffman, Christopher; University Of Washington; Hoffman@math.washington.edu
In [2] Benjamini, Haggstrom, Peres and Steif introduced the model of dynamical random walk on the d-dimensional lattice Z^d. This is a continuum of random walks indexed by a time parameter t. They...
Diameter of Random Cayley Graph of Z_q (2006)
Amir, Gideon, Gurel-Gurevich, Ori
Consider the Cayley graph of the cyclic group of prime order q with k uniformly chosen generators. For k fixed, we prove that the diameter of said graph is asymptotically (in q) of order q^(1/k).
A special set of exceptional times for dynamical random walk on $\Z^2$ (2006)
Amir, Gideon, Hoffman, Christopher
Benjamini,Haggstrom, Peres and Steif introduced the model of dynamical random walk on Z^d. This is a continuum of random walks indexed by a parameter t. They proved that for d=3,4 there almost surely...
On two biased graph processes (2006)
In [Amir et al.], the authors consider the generalization $\Gor$ of the Erd\H{o}s-R\'enyi random graph process $G$, where instead of adding new edges uniformly, $\Gor$ gives a weight of size 1 to...
Giant Components in Biased Graph Processes (2005)
Amir, Gideon, Gurel-Gurevich, Ori, Lubetzky, Eyal, Singer, Amit
A random graph process, $\Gorg[1](n)$, is a sequence of graphs on $n$ vertices which begins with the edgeless graph, and where at each step a single edge is added according to a uniform distribution...
Excited random walk against a wall (2005)
Amir, Gideon, Benjamini, Itai, Kozma, Gady
We analyze random walk in the upper half of a three dimensional lattice which goes down whenever it encounters a new vertex, a.k.a. excited random walk. We show that it is recurrent with an expected...