Fluctuations of the front in a one dimensional model of $X+Y\to 2X$

DOI10.1090/S0002-9947-09-04889-2zbMath1177.82081arXivmath/0607549OpenAlexW4300017790MaRDI QIDQ3642707

Jeremy Quastel, Alejandro F. Ramírez, Francis Comets

Publication date: 6 November 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607549

zbMATH Keywords

front propagationinteracting particle systemsregeneration times

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Interacting particle systems in time-dependent statistical mechanics (82C22) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics (82C24) Renewal theory (60K05)

Related Items (10)

From transience to recurrence with Poisson tree frogs ⋮ Fluctuations of the front in a one-dimensional model for the spread of an infection ⋮ Criticality of a randomly-driven front ⋮ Spread of infections in a heterogeneous moving population ⋮ A stochastic combustion model with thresholds on trees ⋮ Explosion and non-explosion for the continuous-time frog model ⋮ Spread of an infection on the zero range process ⋮ Large deviations of the front in a one-dimensional model of \(X+Y\rightarrow 2X\) ⋮ Laws of large numbers for the frog model on the complete graph ⋮ First passage time of the frog model has a sublinear variance

Cites Work

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• A law of large numbers for random walks in random environment
• The shape theorem for the frog model
• Asymptotic behavior of a stochastic combustion growth process
• The spread of a rumor or infection in a moving population

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