UBC Mathematics Department
Abstract: Linear polymer molecules are modelled by self-avoiding walks and branched polymers are modelled by lattice trees and lattice animals. It is widely believed that the number and typical size of self-avoiding walks and of lattice trees and animals are governed by dimension-dependent universal critical exponents. Similar critical exponents arise in percolation theory, an elementary model of a phase transition of interest in probability theory and statistical mechanics. This lecture, intended for a general mathematical audience, describes joint work with Takashi Hara proving existence of critical exponents for these models in high dimensions, using a method known as the lace expansion.