4 citations · 8 across the 7 of their papers we have counts for
8 papers · 1 filter
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 =…
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…
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…
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…
Ergodicity and Mixing Properties of the Northeast Model
George Kordzakhia, Steven P. Lalley
The Northeast Model is a spin system on the two-dimensional integer lattice that evolves according to the following rule: Whenever a site's southerly and westerly nearest neighbors…
A two-species competition model on Z^d
George Kordzakhia, Steven P. Lalley
We consider a two-type stochastic competition model on the integer lattice Z^d. The model describes the space evolution of two ``species'' competing for territory along their bound…