# The 2010 CRM-Fields-PIMS Prize is awarded to Gordon Slade

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.

In 1992 Hara and Slade proved that in five or more dimensions the end-to-end distanceof self-avoiding walk grows according to the same √n law exhibited by simple random walk and that the scaling limit of self-avoiding walk is Brownian motion.

In 1989 Hara and Slade proved that the Aizenman-Newman triangle condition holds for critical percolation in high dimensions. The triangle condition implies a large collection of properties for the critical cluster that are collectively summarised by the term “mean field theory”. Since this initial impetus a quite complete understanding of critical percolation clusters in high dimensions has grown out of work with his co-authors Derbez, Hara, van der Hofstad and den Hollander. In particular, the scaling limit of oriented percolation is super-Brownian motion and the existence and the properties of the incipient infinité percolation cluster have been established in certain cases. By related methods, Slade and his co-authors