## ISOPERIMETRIC INEQUALITIES AND MIXING TIME FOR A RANDOM WALK ON A RANDOM POINT PROCESS (2006)

Citations: | 6 - 5 self |

### BibTeX

@MISC{Caputo06isoperimetricinequalities,

author = {Pietro Caputo and Alessandra Faggionato},

title = {ISOPERIMETRIC INEQUALITIES AND MIXING TIME FOR A RANDOM WALK ON A RANDOM POINT PROCESS},

year = {2006}

}

### OpenURL

### Abstract

Abstract. 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 process we prove that at α = d there is a transition from diffusive to subdiffusive behavior of the random walk. Key words: Random walk in random environment, point process, isoperimetric inequality, mixing time, isoperimetric profile, percolation.