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Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times
| Content Provider | Semantic Scholar |
|---|---|
| Author | Peres, Yuval Stauffer, Alexandre Steif, Jeffrey E. |
| Copyright Year | 2013 |
| Abstract | We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph $$G$$G are either open or closed and refresh their status at rate $$\mu $$μ while at the same time a random walker moves on $$G$$G at rate 1 but only along edges which are open. On the $$d$$d-dimensional torus with side length $$n$$n, we prove that in the subcritical regime, the mixing times for both the full system and the random walker are $$n^2/\mu $$n2/μ 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 $${\mathbb {Z}}^d$$Zd holds for this model as well. |
| Starting Page | 487 |
| Ending Page | 530 |
| Page Count | 44 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00440-014-0578-4 |
| Volume Number | 162 |
| Alternate Webpage(s) | https://purehost.bath.ac.uk/ws/portalfiles/portal/137195375/Random_Walks.pdf |
| Alternate Webpage(s) | http://www.math.chalmers.se/~steif/p57.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/1308.6193v1.pdf |
| Alternate Webpage(s) | https://www.microsoft.com/en-us/research/wp-content/uploads/2017/01/1308.6193v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s00440-014-0578-4 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
