[ספר][B] What is percolation?

G Grimmett, G Grimmett - 1999‏ - Springer
Suppose we immerse a large porous stone in a bucket of water. What is the probability that
the centre of the stone is wetted? In formulating a simple stochastic model for such a …

[ספר][B] Stochastic interacting systems: contact, voter and exclusion processes

TM Liggett - 2013‏ - books.google.com
Interactive Particle Systems is a branch of Probability Theory with close connections to
Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T …

Percolation and disordered systems

E Giné, GR Grimmett, L Saloff-Coste… - Lectures on Probability …, 1997‏ - Springer
This course aims to be a (nearly) self-contained account of part of the mathematical theory of
percolation and related topics. The first nine chapters summarise rigorous results in …

Stochastic spatial models: a user's guide to ecological applications

R Durrett, SA Levin - … Transactions of the Royal Society of …, 1994‏ - royalsocietypublishing.org
Spatial pattern, how it arises and how it is maintained, are central foci for ecological theory.
In recent years, some attention has shifted from continuum models to spatially discrete …

Coalescing Random Walks and Voter Model Consensus Times on the Torus in Zd

JT Cox - The Annals of Probability, 1989‏ - JSTOR
Let η t be the basic voter model on Z d and let η (N) t be the voter model on Λ (N), the torus of
side N in Z d. Unlike η t, η (N) t (for fixed N) gets trapped with probability 1 as t→∞ at all 0's …

Contact processes on random graphs with power law degree distributions have critical value 0

S Chatterjee, R Durrett - 2009‏ - projecteuclid.org
If we consider the contact process with infection rate λ on a random graph on n vertices with
power law degree distributions, mean field calculations suggest that the critical value λ c of …

Stochastic models of interacting systems

TM Liggett - The Annals of Probability, 1997‏ - projecteuclid.org
Interacting particle systems is by now a mature area of probability theory, but one that is still
very active. We begin this paper by explaining how models from this area arise in fields such …

[PDF][PDF] Limit theorems for the spread of epidemics and forest fires

JT Cox, R Durrett - Stochastic processes and their applications, 1988‏ - core.ac.uk
In this paper we will prove theorems which describe the asymptotic behavior of two closely
related processes: one which has been used ta model the spread of epidemics (Bailey …

Interacting particle systems as stochastic social dynamics

D Aldous - 2013‏ - projecteuclid.org
The style of mathematical models known to probabilists as Interacting Particle Systems and
exemplified by the Voter, Exclusion and Contact processes have found use in many …

Survival and extinction of epidemics on random graphs with general degree

S Bhamidi, D Nam, O Nguyen, A Sly - 2021‏ - projecteuclid.org
In this paper we establish the necessary and sufficient criterion for the contact process on
Galton–Watson trees (resp., random graphs) to exhibit the phase of extinction (resp., short …