Phase transitions for mixing and cover times for random walks

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• Perla Sousi (Cambridge)
• Thursday 23 January 2025, 16:00-17:00
• CMS MR2.

If you have a question about this talk, please contact HoD Secretary, DPMMS.

I will talk about two fundamental quantities for random walks on graphs: mixing and cover times. The mixing time is the time it takes for a random walk to reach equilibrium while the cover time is the time needed for the walk to visit every vertex of the graph at least once. In the first part of the talk, I will focus on the cutoff phenomenon which occurs when the walk converges to equilibrium in an abrupt manner. Even though this is a widespread phenomenon, it remains not fully understood. I will present a universality result in this context. In the second part I will shift to the problem of covering a discrete torus of high dimension by a simple random walk. We will explore a phase transition for the set of vertices that have not been visited at times that are multiples of the expected cover time.

A wine reception will be held in the Central Core following this talk.

This talk is part of the DPMMS Departmental Colloquia series.

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