%0 Journal Article
%T Principal eigenvalue for random walk among random traps on Z^d
%A Jean-Christophe Mourrat
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0805.0706v2