TY - JOUR

T1 - Random walks on dynamical percolation

T2 - mixing times, mean squared displacement and hitting times

AU - Peres, Yuval

AU - Stauffer, Alexandre

AU - Steif, Jeffrey E.

PY - 2015/8

Y1 - 2015/8

N2 - We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph \(G\) are either open or closed and refresh their status at rate \(\mu \) while at the same time a random walker moves on \(G\) at rate 1 but only along edges which are open. On the \(d\)-dimensional torus with side length \(n\), we prove that in the subcritical regime, the mixing times for both the full system and the random walker are \(n^2/\mu \) up to constants. We also obtain results concerning mean squared displacement and hitting times. Finally, we show that the usual recurrence transience dichotomy for the lattice \({\mathbb {Z}}^d\) holds for this model as well.

AB - We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph \(G\) are either open or closed and refresh their status at rate \(\mu \) while at the same time a random walker moves on \(G\) at rate 1 but only along edges which are open. On the \(d\)-dimensional torus with side length \(n\), we prove that in the subcritical regime, the mixing times for both the full system and the random walker are \(n^2/\mu \) up to constants. We also obtain results concerning mean squared displacement and hitting times. Finally, we show that the usual recurrence transience dichotomy for the lattice \({\mathbb {Z}}^d\) holds for this model as well.

UR - http://dx.doi.org/10.1007/s00440-014-0578-4

U2 - 10.1007/s00440-014-0578-4

DO - 10.1007/s00440-014-0578-4

M3 - Article

VL - 162

SP - 487

EP - 530

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 3

ER -