374 citations · 1.2k across the 68 of their papers we have counts for
6 papers · 1 filter
A duality principle for selection games
Lionel Levine, Scott Sheffield, Katherine E. Stange
A dinner table seats k guests and holds n discrete morsels of food. Guests select morsels in turn until all are consumed. Each guest has a ranking of the morsels according to how m…
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…
Quantum gravity and inventory accumulation
Scott Sheffield
We begin by studying inventory accumulation at a LIFO (last-in-first-out) retailer with two products. In the simplest version, the following occur with equal probability at each ti…
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…
Internal DLA and the Gaussian free field
David Jerison, Lionel Levine, Scott Sheffield
In previous works, we showed that the internal DLA cluster on \Z^d with t particles is a.s. spherical up to a maximal error of O(\log t) if d=2 and O(\sqrt{\log t}) if d > 2. This…
Internal DLA in Higher Dimensions
David Jerison, Lionel Levine, Scott Sheffield
Let A(t) denote the cluster produced by internal diffusion limited aggregation (internal DLA) with t particles in dimension d > 2. We show that A(t) is approximately spherical, up…