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Laudatio: The Mathematical Work of Jürgen Gärtner Read chapter Read first chapter

2012 | OriginalPaper | Chapter

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

Authors : Harry Kesten, Alejandro F. Ramı́rez, Vladas Sidoravicius

Published in: Probability in Complex Physical Systems

Publisher: 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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previous chapter Quenched Lyapunov Exponent for the Parabolic Anderson Model in a Dynamic Random Environment
next chapter The Parabolic Anderson Model with Acceleration and Deceleration
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Metadata
Title
Asymptotic Shape and Propagation of Fronts for Growth Models in Dynamic Random Environment
Authors
Harry Kesten
Alejandro F. Ramı́rez
Vladas Sidoravicius
Copyright Year
2012
Publisher
Springer Berlin Heidelberg
Book
Probability in Complex Physical Systems

Print ISBN: 978-3-642-23810-9

Electronic ISBN: 978-3-642-23811-6

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-3-642-23811-6_8