GONVILLE AND CAIUS COLLEGE
G. C. STEWARD LECTURES 2010
A RANDOM WALK THROUGH ANALYSIS, NETWORKS AND BIOLOGY
Professor Ruth J. Williams
G. C. Steward Visiting Fellow
Gonville and Caius College, Cambridge University
Lecture 1: Brownian motion, stochastic calculus and the Dirichlet problem.
For a short article related to this lecture, click here.
Click here for a link to a short note on famous Caian John Venn. This note is taken from "Annotated readings in the history of statistics"
by H. A. David and A. W. F. Edwards; it includes
an excerpt from John Venn's
"Logic of Chance" (Macmillan, 1888) in which
a diagram of a random walk is shown. (Thanks to Professor Anthony Edwards of Gonville and Caius for pointing out this
early publication of such a diagram.)
Lecture 2: Reflecting Brownian motion and queueing networks: an introduction.
Link to java applets for simulating M/M/1 queues and more general queueing networks
with exponential interarrival and service times (by Tom Slater 2000,
linked through Jane Hillston's webpage).
Supplementary reading (beyond the introductory material presented in Lecture 2):
For an expository article on diffusion approximations of queueing networks
For an expository article on reflecting Brownian motions,
An article on reflecting Brownian motion in a
two-dimensional wedge is available here.
Since the two expository articles were written, further progress has been
made on sufficient conditions for approximating multiclass queueing
networks by reflecting Brownian motions. For further reading on this topic,
Sample applications of diffusion approximations to queueing networks and more general stochastic processing networks:
Internet congestion control,
cooperation in wireless communication and control of road traffic.
Lecture 3: Queues and Biology.
A paper related to the theoretical model presented in this lecture is available by clicking here
and a related experimental paper is available by
(in both cases, it is advised to download both the
paper and the supplement).
Last updated December 20, 2011.