## Math Talks: "The range of deterministic random walks," Laura Florescu ‘11 (Courant Institute of Mathematical Sciences, New York University)

Thursday, March 5, 4:10 PM - 5:00 PM

Physics 123

This event is open to the public.

LECTURE

Laura Florescu ‘11, Courant Institute of Mathematical Sciences, New York University

Mathematics Talk: *The range of deterministic random walks*

Thursday, March 5, 2015, 4:10 p.m., Physics 123

In a deterministic random walk on a graph, the exits from each vertex follow a prescribed periodic sequence. We show that any such walk on the $d$-dimensional lattice $\Z^d$ visits at least on the order of $t^{d/(d+1)}$ distinct sites in $t$ steps. In a uniform deterministic random walk the first exit from each vertex is to a neighbor chosen uniformly at random. We prove a shape theorem for the uniform walk on the comb graph, showing that the range is of order $t^{2/3}$ and the asymptotic shape of the range is a diamond. Using a connection to the mirror model we show that the uniform rotor walk is recurrent on two different directed graphs obtained by orienting the edges of the square grid, the Manhattan lattice and the $F$-lattice. Joint work with Lionel Levine and Yuval Peres.

**All are welcome. Free and open to the public. Refreshment will be provided.**

For more information, visit:

http://www.reed.edu/math/seminars/index.html.*Submitted by Kim Kadas.**Posted on Feb 25, 2015*

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