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Investigation of a Random Walk on a Dynamical Random Graph

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We investigate properties of a simple random walk X on a dynamically evolving graph \eta. We’ll work on the complete graph, and for each edge, at rate 1 we resample its state: w.p. p it is open and w.p. 1-p closed. We’ll take p = c/n for a constant c. The graph will (typically) be sparse, with ‘most’ vertices degree order 1. In particular, we’ll determine upper bounds on how long it takes a walk to become isolated. This will allow us to couple two full systems (X,\eta) and (Y,\xi), which in particular gives us a bound on the mixing time of the full system. This is joint work with my supervisor, Perla Sousi.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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