Biased random walk on dynamical percolation
- We study biased random walks on dynamical percolation on Zd. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and we investigate the speed of the walk as a function of the bias. While for d=1 the speed is increasing, we show that, in general, this fails in dimension d≥2. As our main result, we establish two regimes of parameters, separated by an explicit critical curve such that the speed is either eventually strictly increasing or eventually strictly decreasing. This is in sharp contrast to the biased random walk on a static supercritical percolation cluster where the speed is known to be eventually zero.
| Author: | Sebastian Andres, Nina Gantert, Dominik SchmidGND, Perla Sousi |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/123083 |
| ISSN: | 0091-1798OPAC |
| Parent Title (English): | The Annals of Probability |
| Publisher: | Institute of Mathematical Statistics |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2024 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/06/26 |
| Volume: | 52 |
| Issue: | 6 |
| First Page: | 2051 |
| Last Page: | 2078 |
| DOI: | https://doi.org/10.1214/23-aop1679 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
