Simple random walk is well understood. However,
if we condition a random walk not to intersect itself, so
that it is a self-avoiding walk, then it is much more difficult
to analyze and many of the important mathematical problems
remain unsolved.
This lecture will give an overview of some of what is known
about the self-avoiding walk, including some old and some
more recent results, using methods that touch on combinatorics,
probability, and statistical
mechanics.
Audio & Slides of the Talk
The Directors of the three Institutes, CRM, Fields and
PIMS, are pleased to announce that Gordon Slade from the
University of British Columbia is the recipient of the 2010
CRM-Fields-PIMS Prize. The award recognises his outstanding
work in rigorous statistical mechanics and probability.
He is renowned for developing a technique known as the lace
expansion into a systematic calculus which he has applied
to diverse and famous problems including self-avoiding walk,
percolation, branched polymers, random graphs, and numerical
techniques for the exact enumeration of self-avoiding walks.
His results address some of the most difficult problems
in central areas of probability and statistical physics.
These are questions motivated by physical problems which
are easy to state (what is the average length of an n-step
self-avoiding walk?), but notoriously difficult to solve.
Gordon Slade received his undergraduate degree from the
University of Toronto in 1977 and completed his Doctoral
degree with Lon Rosen and Joel Feldman at the University
of British Columbia in 1984. He was Lecturer at the University
of Virginia from 1985 to 1986. In 1986 he joined the faculty
of McMaster University and since 1999 he has been Professor
of Mathematics at the University of British Columbia.
Gordon Slade has been a leader in Canadian Mathematics,
having been an organiser of the (98-99) thematic year in
probability and its applications at the Fields Institute,
co-organiser of the recent CRM-PIMS Programme Challenges
and Perspectives in Probability (08-09). He has served on
scientific panels of the Fields and Pacific Institutes and
is currently a member of the Editorial Board of the Canadian
Journal of Mathematics. His stature as one of the world's
leading probabilists and mathematical physicists was underlined
by his 1994 invitation to the International Congress of
Mathematics and his 2004 invitation to lecture at the prestigious
St. Flour Summer School.
