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2012 | OriginalPaper | Buchkapitel

Asymptotic Shape and Propagation of Fronts for Growth Models in Dynamic Random Environment

verfasst von : Harry Kesten, Alejandro F. Ramı́rez, Vladas Sidoravicius

Erschienen in: Probability in Complex Physical Systems

Verlag: Springer Berlin Heidelberg

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Abstract

We survey recent rigorous results and open problems related to models of Interacting Particle Systems which describe the autocatalytic type reaction A+B→2B, with diffusion constants of particles being respectively D A ≥0 and D B ≥0. Depending on the choice of the values of D A and D B , we cover three distinct cases: the so called “rumor or infection spread” model (D A >0,D B >0); the Stochastic Combustion process (D A =0 and D B >0); and finally the “modified” Diffusion Limited Aggregation, which corresponds to the case D A >0, D B =0 with modified transition rule: A+B→2B occurs when an A- and a B-particles become nearest neighbors and the A-particle attempts to jump on a vertex where the B-particle is located. Then such jump is suppressed, and A-particle becomes B-particle.

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Metadaten
Titel
Asymptotic Shape and Propagation of Fronts for Growth Models in Dynamic Random Environment
verfasst von
Harry Kesten
Alejandro F. Ramı́rez
Vladas Sidoravicius
Copyright-Jahr
2012
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-23811-6_8