Dept. of Mathematical Sciences |
Spring 2001, UAF (1/23/01) |

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Graduate Seminar in Random Walks (Math 692)

Organizer: **Ed Bueler**

Tentative time & place: **Thursday 2:15--3:15
Chapman 107**
**I propose:** a seminar in random walks, which is a topic
at the intersection of
*probability*, *graph theory* and *analysis*.

A random walk is a sequence of graph--valued random variables which
describe a particle moving from vertex to vertex on a graph according to
a prescribed rule.

A fundamental and typical question is: for a given random walk starting
at a certain point, what is the probability of returning eventually to
that same point? For a surprisingly large class of random walks this
probability is one! Answering this question for a given random walk
is a route to giving a *geometry* to a graph.
My intention is to start by collecting a set of readings in the early
(mathematically and chronologically) theory. Reading, discussing,
and lecturing on these would form the first half of the course.

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Students who want 1.0 credit

should be prepared to give two (2) one--hour talks. Topics for such
talks can and should include:

(i) lectures on the content of research papers in
random walks and associated areas, and

(ii) descriptions of simulations of random walks
performed by the student.

Graduate students in mathematics and statistics are especially encouraged
to attend.

**Contact Ed Bueler at ffelb@uaf.edu or x7693 or Chapman
301C.**

**The first meeting on Thursday Jan. 25 will include setting up a
permanent time!**