3:30 p.m., Friday
Remco van der Hofstad
Recent progress in one-dimensional and high-dimensional statistical mechanical models
In this talk, I will summarize recent progress made in a
number of statistical mechanical models, such as the
self-avoiding walk and percolation. Self-avoiding walks
are a model for polymers, whereas percolation can be used
to study the flow of fluids through porous media. Progress
has mainly been made in dimension one and high dimensions.
In high dimensions, this progress is mainly due to the
use of the lace expansion. In dimension one, the lace
expansion can also be used. However, most progress
is made using large deviation techniques. This talk will
be panoramic, in the sense that it will highlight the
new developments, and give a flavour of the proofs
rather than the technical details.
The talk is based upon joint work with Takashi Hara,
Frank den Hollander, Wolfgang Koenig and Gordon Slade.