Projects per year
Abstract
We study the mixing time of a random walker who moves inside a dynamical random cluster model on the d-dimensional torus of side-length n. In this model, edges switch at rate \mu between open and closed, following a Glauber dynamics for the random cluster model with parameters p,q. At the same time, the walker jumps at rate 1 as a simple random walk on the torus, but is only allowed to traverse open edges. We show that for small enough p the mixing time of the random walker is of order n^2/\mu. In our proof we construct of a non-Markovian coupling through a multi-scale analysis of the environment, which we believe could be more widely applicable.
Original language | English |
---|---|
Publisher | arXiv |
Number of pages | 52 |
Publication status | Published - 7 Sept 2022 |
Keywords
- math.PR
- cs.DM
Fingerprint
Dive into the research topics of 'Mixing time of random walk on dynamical random cluster'. Together they form a unique fingerprint.Projects
- 1 Finished
-
Early Career Fellowship - Mathematical Analysis of Strongly Correlated Processes on Discrete Dynamic Structures
Stauffer, A. (PI)
Engineering and Physical Sciences Research Council
1/04/16 → 30/09/22
Project: Research council