arXiv subjects

Ron Rosenthal

Publications and source records attributed to Ron Rosenthal.

21 records · Page 2Linked to original sources

arXiv2012

The need for speed : Maximizing random walks speed on fixed environments

We study nearest neighbor random walks on fixed environments of $\mathbb{Z}$ composed of two point types : $(1/2,1/2)$ and $(p,1-p)$ for $p>1/2$. We show that for every environment with density of $p$ drifts bounded by $λ$ we have $\limsup_{n\rightarrow\infty}\frac{X_n}{n}\leq (2p-1)λ$, where $X_n$ is a random walk on the environment. In addition up to some integer effect the environment which gives the best speed is given by equally spaced drifts.

math.PR↗

arXiv2011

Concentration estimates for the isoperimetric constant of the super critical percolation cluster

We consider the Cheeger constant $ϕ(n)$ of the giant component of supercritical bond percolation on $\mathbb{Z}^d/n\mathbb{Z}^d$. We show that the variance of $ϕ(n)$ is bounded by $\fracξ{n^d}$, where $ξ$ is a positive constant that depends only on the dimension $d$ and the percolation parameter.

math.PR↗

arXiv2011

Random walk on discrete point processes

We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the d coordinate directions). We prove that the velocity of such random walks is almost surely 0, and give partial characterization of transience and recurrence for the different dimensions. Finally we prove Central Limit Theorem for such random walks, under a condition on the distance between nearest coordinate nearest points.

math.PR↗