Intermittency on catalysts: symmetric exclusion

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dc.creatorGaertner, J.
dc.creatorHollander, F. den
dc.creatorMaillard, G.
dc.date2006-05-24
dc.date.accessioned2026-07-07T07:14:31Z
dc.date.available2026-07-07T07:14:31Z
dc.descriptionWe continue our study of intermittency for the parabolic Anderson equation $\partial u/\partial t = κΔu + ξu$, where $u\colon \Z^d\times [0,\infty)\to\R$, $κ$ is the diffusion constant, $Δ$ is the discrete Laplacian, and $ξ\colon \Z^d\times [0,\infty)\to\R$ is a space-time random medium. The solution of the equation describes the evolution of a ``reactant'' $u$ under the influence of a ``catalyst'' $ξ$. In this paper we focus on the case where $ξ$ is exclusion with a symmetric random walk transition kernel, starting from equilibrium with density $ρ\in (0,1)$. We consider the annealed Lyapunov exponents, i.e., the exponential growth rates of the successive moments of $u$. We show that these exponents are trivial when the random walk is recurrent, but display an interesting dependence on the diffusion constant $κ$ when the random walk is transient, with qualitatively different behavior in different dimensions. Special attention is given to the asymptotics of the exponents for $κ\to\infty$, which is controlled by moderate deviations of $ξ$ requiring a delicate expansion argument. In Gärtner and den Hollander \cite{garhol04} the case where $ξ$ is a Poisson field of independent (simple) random walks was studied. The two cases show interesting differences and similarities. Throughout the paper, a comparison of the two cases plays a crucial role.
dc.description53 pages
dc.identifierhttps://arxiv.org/abs/math/0605657
dc.identifierhttp://arxiv.org/abs/math/0605657
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112904
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60H25; 82C44
dc.titleIntermittency on catalysts: symmetric exclusion
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