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 -
