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- W2949331301 abstract "We consider the long-time behaviour of a branching random walk in random environment on the lattice $Z^d$. The migration of particles proceeds according to simple random walk in continuous time, while the medium is given as a random potential of spatially dependent killing/branching rates. The main objects of our interest are the annealed moments $ $, i.e., the $p$-th moments over the medium of the $n$-th moment over the migration and killing/branching, of the local and global population sizes. For $n=1$, this is well-understood cite{GM98}, as $m_1$ is closely connected with the parabolic Anderson model. For some special distributions, cite{A00} extended this to $ngeq2$, but only as to the first term of the asymptotics, using (a recursive version of) a Feynman-Kac formula for $m_n$. In this work we derive also the second term of the asymptotics, for a much larger class of distributions. In particular, we show that $ $ and $ $ are asymptotically equal, up to an error $e^{o(t)}$. The cornerstone of our method is a direct Feynman-Kac-type formula for $m_n$, which we establish using the spine techniques developed in cite{HR11}." @default.
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- W2949331301 date "2012-08-01" @default.
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- W2949331301 title "Moment asymptotics for branching random walks in random environment" @default.
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