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Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times

Random walks on dynamical percolation

Yuval Peres ; Alexandre Stauffer ; Jeffrey Steif (Institutionen för matematiska vetenskaper, matematik)
Probability theory and related fields (0178-8051). Vol. 162 (2015), 3, p. 487-530.
[Artikel, refereegranskad vetenskaplig]

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 Z^d holds for this model as well.

Nyckelord: Percolation, dynamical percolation, random walk, mixing times

Denna post skapades 2015-08-31. Senast ändrad 2015-09-11.
CPL Pubid: 221480


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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