374 citations · 1.8k across the 64 of their papers we have counts for
6 papers · 2 filters
Recurrence of Distributional Limits of Finite Planar Graphs
Itai Benjamini, Oded Schramm
Suppose that is a sequence of finite connected planar graphs, and in each a special vertex, called the root, is chosen randomly-uniformly. We introduce the notion of a…
The Dimension of the Planar Brownian Frontier is 4/3
Gregory F. Lawler, Oded Schramm, Wendelin Werner
In a series of recent preprints, we have proven that with probability one the Hausdorff dimension on the outer boundary of planar Brownian motion is 4/3, confirming a conjecture by…
Analyticity of intersection exponents for planar Brownian motion
Gregory F. Lawler, Oded Schramm, Wendelin Werner
We show that the intersection exponents for planar Brownian motions are analytic. More precisely, let and be independent planar Brownian motions started from distinct poin…
Values of Brownian intersection exponents III: Two-sided exponents
Gregory F. Lawler, Oded Schramm, Wendelin Werner
This paper determines values of intersection exponents between packs of planar Brownian motions in the half-plane and in the plane that were not derived in our first two papers. Fo…
Values of Brownian intersection exponents II: Plane exponents
Gregory F. Lawler, Oded Schramm, Wendelin Werner
We derive the exact value of intersection exponents between planar Brownian motions or random walks, confirming predictions from theoretical physics by Duplantier and Kwon. Let B a…
On the cover time of planar graphs
Johan Jonasson, Oded Schramm
The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all the vertices. It is known that the cover time o…