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Abstract
We study the mixing time of a random walker who moves inside a dynamical random cluster model on the ddimensional torus of sidelength 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 nonMarkovian coupling through a multiscale 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
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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.
Engineering and Physical Sciences Research Council
1/04/16 → 30/09/22
Project: Research council