Coloured self-avoiding walks

Self-avoiding walks have been studied, partially because they can be regarded as models of linear polymer molecules. If the vertices of the walks are coloured (A or B, say), they can be regarded as models of copolymers in which the two types of monomers (A and B) behave differently. The colouring can be periodic (eg ABABAB...) or random (eg vertices are coloured independently, A with probability p and B with probability 1-p). Phase transitions in such systems are signalled by singularities in the free energy and the location of the singularity can depend on the colouring. In the random case interest centres on self-averaging phenomena, in which one is interested in questions like ``Do almost all colourings give rise to almost the same value of some property of the walks?". Recent results on both types of colouring will be presented.

Refreshments will be served in Math Annex Room 1115, 3:15 p.m.