Isoperimetric inequalities and mixing time for a random walk on a random point process

Pietro Caputo, Alessandra Faggionato
2007 The Annals of Applied Probability  
We consider the random walk on a simple point process on R^d, d≥2, whose jump rates decay exponentially in the α-power of jump length. The case α =1 corresponds to the phonon-induced variable-range hopping in disordered solids in the regime of strong Anderson localization. Under mild assumptions on the point process, we show, for α∈(0,d), that the random walk confined to a cubic box of side L has a.s. Cheeger constant of order at least L^-1 and mixing time of order L^2. For the Poisson point
more » ... cess, we prove that at α=d, there is a transition from diffusive to subdiffusive behavior of the mixing time.
doi:10.1214/07-aap442 fatcat:apts3gp73bfotk56y7qtcuz42y