Abstract
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.
Original language  English 

Pages (fromto)  487530 
Number of pages  44 
Journal  Probability Theory and Related Fields 
Volume  162 
Issue number  3 
Early online date  9 Sep 2014 
DOIs  
Publication status  Published  Aug 2015 
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Alexandre Stauffer
Person: Research & Teaching