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SUMMARY:Mixing time of random walk on the small-world network - Andjela Sa
 rkovic (Cambridge)
DTSTART:20251028T140000Z
DTEND:20251028T150000Z
UID:TALK240004@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Recently\, there has been an increasing interest in studying m
 ixing properties of random walks on random graphs that have an underlying 
 structure and some smaller random perturbation.\nIn this talk\, we will co
 nsider a ‘small-world network model’ introduced by Dyer et al\, which 
 is meant to resemble real-world networks with an underlying spatial struct
 ure and random connections whose probability decays with distance. We star
 t with a d-dimensional torus of side length n\, and for each pair (x\,y) o
 f different vertices\, we add an edge between them with probability Z/|x-y
 |^d independently\, where\nZ is chosen such that the expected number of ad
 ded edges is 1 for each vertex. We study a simple random walk on this rand
 om graph in at least 3 dimensions\, and we show that with high probability
 \, its mixing time is of order log n\, and there is no cutoff.\n\nJoint wo
 rk with Zsuzsanna Baran\, Jonathan Hermon\, Allan Sly and Perla Sousi 
LOCATION:MR12
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