4:30–5:30 pm
Math/Stat 112

5727 South University Avenue

Reception following the lecture at 5:30 pm in the Reading Room, Math/Stat 101, 5727 South University Avenue

**BILLINGSLEY LECTURES ON PROBABILITY**

RUSSELL LYONS, Department of Mathematics, Indiana University

"Voronoi Tessellations without Nuclei"

#### Also, Prof. Lyons will give the following talk:

Probability and Statistical Physics Seminar

Friday, May 19th, at 2:30 PM, in Eckhart 202, 5734 S. University Avenue

"Monotonicity for Continuous-Time Random Walks"

Abstract: Variable-speed, continuous-time random walk on a graph is given by an assignment of nonnegative rates to its edges. There are independent Poisson processes associated to the edges with the given rates. When a walker is at a vertex, it jumps to a neighbor at the time of the next event that occurs for the corresponding incident edges. In the case of a Cayley graph of a finitely generated group, we are particularly interested in the setting where the edge rates depend only on the corresponding generators. Our lecture is concerned with monotonicity in the rates for various fundamental properties of random walks. We will survey results, counterexamples, and open questions. We will give general ideas of proofs, but avoid technicalities. Most of the talk will be devoted to two questions on Cayley graphs: On infinite graphs, we ask about the limiting linear rate of escape, i.e., the limit of the distance divided by the time. Does this increase when the rates are increased? On finite graphs, we ask about the convergence to the stationary (uniform) distribution. Does this happen faster when the rates are increased? It turns out that both questions have surprising answers. This is joint work with Graham White.

## Event Type

**May**

**18**