374 citations · 1.8k across the 64 of their papers we have counts for
69 papers
Oriented Random Walk on the Heisenberg Group and Percolation
Itai Benjamini, Oded Schramm
It is shown that oriented random walk on the Heisenberg group admits exponential intersection tail. As a corollary we get that on any transitive graph of polynomial volume growth,…
Finitary Coloring
Alexander E. Holroyd, Oded Schramm, David B. Wilson
Suppose that the vertices of are assigned random colors via a finitary factor of independent identically distributed (iid) vertex-labels. That is, the color of vert…
The scaling limits of the Minimal Spanning Tree and Invasion Percolation in the plane
Christophe Garban, Gábor Pete, Oded Schramm
We prove that the Minimal Spanning Tree and the Invasion Percolation Tree on a version of the triangular lattice in the complex plane have unique scaling limits, which are invarian…
The scaling limits of near-critical and dynamical percolation
Christophe Garban, Gábor Pete, Oded Schramm
We prove that near-critical percolation and dynamical percolation on the triangular lattice have a scaling limit as the mesh , in the "quad-crossing" space $\…
Local time on the exceptional set of dynamical percolation, and the Incipient Infinite Cluster
Alan Hammond, Gábor Pete, Oded Schramm
In dynamical critical site percolation on the triangular lattice or bond percolation on \Z^2, we define and study a local time measure on the exceptional times at which the origin…
Unimodular Random Trees
Itai Benjamini, Russell Lyons, Oded Schramm
We consider unimodular random rooted trees (URTs) and invariant forests in Cayley graphs. We show that URTs of bounded degree are the same as the law of the component of the root i…