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

Abstract

Let $({\tau }_x{)}_{x\in {\mathbb{Z}}^d}$ 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 ${\mathbb{Z}}^d$. 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.

17 pages, v2: simplified proofs in section 3

References in corpus (2)

• K-processes, scaling limit and aging for the trap model in the complete graph
• Quenched scaling limits of trap models