9 citations · 56 across the 26 of their papers we have counts for
4 papers · 1 filter
Random Walk on a Surface Group: Boundary Behavior of the Green's Function at the Spectral Radius
Steven P. Lalley
It is proved that the Green's function of the simple random walk on a surface group of large genus decays exponentially at the spectral radius. It is also shown that Ancona's inequ…
Critical scaling of stochastic epidemic models
Steven P. Lalley
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent coin tosses. Spatial…
Occupation Statistics of Critical Branching Random Walks in Two or Higher Dimensions
Steven Lalley, Xinghua Zheng
Consider a critical nearest neighbor branching random walk on the -dimensional integer lattice initiated by a single particle at the origin. Let be the event that the br…
Spatial Epidemics: Critical Behavior in One Dimension
Steven P. Lalley
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent p-coin tosses. Spatial v…