Annealed asymptotics for the parabolic Anderson model with a moving catalyst

J. Gärtner, M.O. Heydenreich

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

11 Citaten (Scopus)


This paper deals with the solution u to the parabolic Anderson equation ¿u/¿t=¿¿u+¿u on the lattice . We consider the case where the potential ¿ is time-dependent and has the form ¿(t,x)=d0(x-Yt) with Yt being a simple random walk with jump rate 2d. The solution u may be interpreted as the concentration of a reactant under the influence of a single catalyst particle Yt. In the first part of the paper we show that the moment Lyapunov exponents coincide with the upper boundary of the spectrum of certain Hamiltonians. In the second part we study intermittency in terms of the moment Lyapunov exponents as a function of the model parameters ¿ and .
Originele taal-2Engels
Pagina's (van-tot)1511-1529
TijdschriftStochastic Processes and their Applications
Nummer van het tijdschrift11
StatusGepubliceerd - 2006

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