Principal eigenvalue for random walk among random traps on Z^d

Details Principal eigenvalue for random walk among random traps on Z^d Principal eigenvalue for random walk among random traps on Z^d

2008-05-06

arxiv.org/abs/0805.0706v2

Mathematics

Probability

17 pages, v2: simplified proofs in section 3

Scientific paper

Let $(\tau_x)_{x \in \Z^d}$ be i.i.d. random variables with heavy (polynomial) tails. Given $a \in [0,1]$, we consider the Markov process defined by the jump rates $\omega_{x \to y} = {\tau_x}^{-(1-a)} {\tau_y}^a$ between two neighbours $x$ and $y$ in $\Z^d$. We give the asymptotic behaviour of the principal eigenvalue of the generator of this process, with Dirichlet boundary condition. The prominent feature is a phase transition that occurs at some threshold depending on the dimension.

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