Long-time properties of trapping on fractals

Abstract

We investigate the long-time decay behaviour of a nearest-neighbour random walker which gets trapped at the first encounter of a sink. We consider both regular and fractal lattices and establish for compact exploration the asymptotic decay Φ ∼ exp[ — Ctα] with α ≡ d/(d + 2) where d is the spectral dimension. The numerical simulations support the Φ structure, but with a larger α for both the square lattice and the d = 1.365 Sierpinski gaske