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

  • Harry Kesten
  • Alejandro F. Ramı́rez
  • Vladas Sidoravicius
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 11)

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.

Keywords

Regeneration Time Time Path Large Deviation Principle Simple Random Walk Jump Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

A.F.R and V.S. would like to thank the all organizers of both workshops and in particular to Prof. Wolfgang König for his hospitality. A.F.R. would like to thank the support of FONDECYT grant 1100298.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Harry Kesten
    • 1
  • Alejandro F. Ramı́rez
    • 2
  • Vladas Sidoravicius
    • 3
  1. 1.Department of MathematicsCornell UniversityIthacaUSA
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileMacul SantiagoChile
  3. 3.IMPARio de JaneiroBrazil

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