GONVILLE AND CAIUS COLLEGE
CAMBRIDGE, UK

G. C. STEWARD LECTURES 2010



A RANDOM WALK THROUGH ANALYSIS, NETWORKS AND BIOLOGY
by
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 click here.
    For an expository article on reflecting Brownian motions, click here. 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, click here.
    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 clicking here (in both cases, it is advised to download both the paper and the supplement).
    Last updated December 20, 2011.