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[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 …
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 …
Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T …
Percolation and disordered systems
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 …
percolation and related topics. The first nine chapters summarise rigorous results in …
Stochastic spatial models: a user's guide to ecological applications
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 …
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
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 …
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 …
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 …
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
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 …
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 …
exemplified by the Voter, Exclusion and Contact processes have found use in many …
Survival and extinction of epidemics on random graphs with general degree
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 …
Galton–Watson trees (resp., random graphs) to exhibit the phase of extinction (resp., short …