Probability seminar: Self-interacting random walks

30 October 2015, 3.30 PM - 30 October 2015, 4.30 PM

Perla Sousi, Cambridge

SM3, School of Mathematics

Perla Sousi, Cambridge

Self-interacting random walks

Take two 3-dimensional probability measures in three dimensions with mean 0. At each time we choose one of the measures based on the history of the process and take a step according to that measure. (For instance, we might use the first measure  at a newly visited site, and the second measure at sites that have been visited before). Benjamini, Kozma and Schapira asked if the resulting process must be transient, or could it be recurrent? In this talk I will present the answer and sketch the proof. Perhaps surprisingly, the answer changes when we have 3 measures instead of 2.

Consider another zero mean walk in three dimensions, where on the first visit to a vertex it moves vertically and on later visits to the same vertex horizontally. Is this transient or recurrent? I will answer this question by relating it to a dispersion result for martingales.

(Based on joint works with Yuval Peres, Serguei Popov and Bruno Schapira)

Contact information

Organisers: Marton Balazs, Haeran Cho

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