14th Northwest Probability Seminar – The star-triangle transformation in probability theory


October 19, 2012


The star-triangle transformation was `discovered’ in 1899. It has since become one of the basic tools for studying disordered systems in two dimensions, and it is known amongst physicists as the `Yang-Baxter equation’. We shall explain its harmony with de Bruijn’s theory of tilings and isoradial graphs, as developed by Kenyon and co-authors. Then we outline its use in proving universality for percolation in two dimensions.