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math.PR2009
A Geometric Interpretation of Half-Plane Capacity
Steven Lalley, Gregory Lawler, Hariharan Narayanan
Let A be a bounded, relatively closed subset of the upper half plane H whose complement C is simply connected. If B_t is a standard complex Brownian motion starting at iy and t_A =…
math.PR2009
Spatial Epidemics and Local Times for Critical Branching Random Walks in Dimensions 2 and 3
Steven P. Lalley, Xinghua Zheng
The behavior at criticality of spatial SIR (susceptible/infected/recovered) epidemic models in dimensions two and three is investigated. In these models, finite populations of size…