Mathematics Colloquium

Random growth off a one dimensional substrate is often described by the Kardar-Parisi-Zhang stochastic partial differential equation.  

It is a member of a large universality class characterized by unusual fluctuations, some of which appeared earlier in random matrix theory.  

On large space time scales, the fluctuations in the class turn out to be described by a special scaling invariant Markov process — the KPZ fixed point — obtained through the solution of a special discrete model, TASEP.  Both turn out to be new integrable systems, leading to unexpected connections between random growth and classical integrable partial differential equations.