Tom Hutchcroft

Scaling inequalities in percolation

The scaling relations are equalities relating critical exponents that are expected to hold in essentially any statistical mechanics model undergoing a continuous phase transition. Although regarded by physicists as essentially a triviality, their rigorous derivation (even conditional on the existence of exponents) is a major open problem for mathematicians. In this talk, I will survey the heuristics behind the scaling relations and the partial results that have been proven rigorously for percolation. In particular, I will sketch a proof of two new rigorous scaling inequalities that can be proven using the theory of randomized algorithms and the OSSS inequality.