87 citations · 264 across the 36 of their papers we have counts for
6 papers · 1 filter
Random Graph-Homomorphisms and Logarithmic Degree
Itai Benjamini, Ariel Yadin, Amir Yehudayoff
A graph homomorphism between two graphs is a map from the vertex set of one graph to the vertex set of the other graph, that maps edges to edges. In this note we study the range of…
Geodesics and almost geodesic cycles in random regular graphs
Itai Benjamini, Carlos Hoppen, Eran ofek +2
A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every…
Submean variance bound for effective resistance of random electric networks
Itai Benjamini, Raphael Rossignol
We study a model of random electric networks with Bernoulli resistances. In the case of the lattice Z^2, we show that the point-to-point effective resistance between 0 and a vertex…
For what number of cars must self organization occur in the Biham-Middleton-Levine traffic model from any possible starting configuration?
Tim D. Austin, Itai Benjamini
For any initial configuration of fewer than N/2 cars the BML model will self organize to attain speed one. On the other hand, there is a configuration of size m in which no car can…
On the range of the simple random walk bridge on groups
Itai Benjamini, Roey Izkovsky, Harry Kesten
Let G be a vertex transitive graph. A study of the range of simple random walk on G and of its bridge is proposed. While it is expected that on a graph of polynomial growth the siz…
Recurrence of random walk traces
Itai Benjamini, Ori Gurel-Gurevich, Russell Lyons
We show that the edges crossed by a random walk in a network form a recurrent graph a.s. In fact, the same is true when those edges are weighted by the number of crossings.