374 citations · 1.2k across the 68 of their papers we have counts for
4 papers · 1 filter
The natural parametrization for the Schramm-Loewner evolution
Gregory F. Lawler, Scott Sheffield
The Schramm-Loewner evolution (SLE_κ) is a candidate for the scaling limit of random curves arising in two-dimensional critical phenomena. When κ< 8, an instance of SLE_κis a rando…
Fixation for Distributed Clustering Processes
Marcelo R. Hilario, Oren Louidor, Charles M. Newman +3
We study a discrete-time resource flow in , where wealthier vertices attract the resources of their less rich neighbors. For any translation-invariant probability distribution…
Power law Polya's urn and fractional Brownian motion
Alan Hammond, Scott Sheffield
We introduce a natural family of random walks on the set of integers that scale to fractional Brownian motion. The increments X_n have the property that given {X_k: k < n}, the con…
Duality and KPZ in Liouville Quantum Gravity
Bertrand Duplantier, Scott Sheffield
We present a (mathematically rigorous) probabilistic and geometrical proof of the KPZ relation between scaling exponents in a Euclidean planar domain D and in Liouville quantum gra…