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

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.

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 or x7693 or Chapman 301C.
The first meeting on Thursday Jan. 25 will include setting up a permanent time!