374 citations · 1.2k across the 68 of their papers we have counts for
5 papers · 1 filter
Tug-of-war and infinity Laplace equation with vanishing Neumann boundary condition
Tonći Antunović, Yuval Peres, Scott Sheffield +1
We study a version of the stochastic "tug-of-war" game, played on graphs and smooth domains, with the empty set of terminal states. We prove that, when the running payoff function…
Absolute continuity of Brownian bridges under certain gauge transformations
Andrea R. Nahmod, Luc Rey-Bellet, Scott Sheffield +1
We prove absolute continuity of Gaussian measures associated to complex Brownian bridges under certain gauge transformations. As an application we prove that the invariant measure…
Vector-valued optimal Lipschitz extensions
Scott Sheffield, Charles K. Smart
Consider a bounded open set in and a Lipschitz function g from the boundary of to . Does this function always have a canonical optimal Lipschitz extension to all…
Tug of war with noise: a game theoretic view of the p-Laplacian
Yuval Peres, Scott Sheffield
Fix a bounded domain Omega in R^d, a continuous function F on the boundary of Omega, and constants epsilon>0, p>1, and q>1 with p^{-1} + q^{-1} = 1. For each x in Omega, let u^epsi…
Tug-of-war and the infinity Laplacian
Yuval Peres, Oded Schramm, Scott Sheffield +1
We prove that every bounded Lipschitz function F on a subset Y of a length space X admits a tautest extension to X, i.e., a unique Lipschitz extension u for which Lip_U u = Lip_{bo…