16 papers
The Uniform Gromov Hausdorff Gap Problem for Approximating Spheres by Finite Homogeneous Spaces
Itai Benjamini
Let be the unit round sphere with its intrinsic angular metric, normalized so that . For finite homogeneous metric spaces , put \[ δ_n=\inf_X d…
The Conclave Process
Itai Benjamini, Zhenhao Cai, Guanyi Chen +2
We introduce a stochastic model for the papal conclave in which cardinals vote repeatedly among themselves until one cardinal receives all the votes. In each round, the probabi…
The number of tiles of
Itai Benjamini, Gady Kozma, Elad Tzalik
It is proved that the number of subsets of that tile is .
How fast does the range of simple random walk grow?
Itai Benjamini, Justin Salez
Consider a discrete-time simple random walk on an infinite, connected, locally finite simple graph , and let \[ R_t := |\{X_0,\ldots,X_t\}| \] denote its range.…
Euclidean vs Graph Metric: The Fixed-Source Problem
Itai Benjamini
We prove that two fixed sources in the Euclidean plane can be realized by a bounded-degree planar unit-edge graph on a 10-net, with graph distance from each source agreeing with Eu…
The Pile Process on a Cycle
Itai Benjamini, Eric Shellef
Consider a finite particle system in which, at each step, one particle from a vertex with a lower neighboring vertex moves to a neighboring vertex of minimum height. For the cycle…