Kardar–Parisi–Zhang Universality

[摘要] Universality in complex random systems is a striking concept that has played a central role in the direction of research within probability, mathematical physics and statistical mechanics. In this article, we will describe how a variety of physical systems and mathematical models, includingrandomly growing interfaces, certain stochastic PDEs, traffic models, paths in random environments and random matrices, all demonstrate the same universal statistical behavioursin their long-time/large-scale limit. These systems are saidto lie in the Kardar–Parisi–Zhang (KPZ) universality class.Proof of universality within these classes of systems (exceptfor random matrices) has remained mostly elusive. Extensivecomputer simulations, non-rigorous physical arguments andheuristics, some laboratory experiments and limited mathematically rigorous results provide important evidence for thisbelief.