Probability Seminar: Alexander Tomberg

We calculate the logarithmic correction to the decay of the critical two-point function for networks of p mutually-avoiding weakly self-avoiding walks joining two distant points on the 4-dimensional integer lattice. While similar results have been obtained previously for dimensions d > 4 by lace expansion, our proof is based on a rigorous renormalisation group analysis of a representation of the self-avoiding walk as a supersymmetric field theory. The talk is based on joint and ongoing work with Roland Bauerschmidt, David Brydges and my supervisor Gordon Slade.