Kardar-Parisi-Zhang Equation and Universality

Abstract

Polymer models belong to Kardar-Parisi-Zhang (KPZ) universality class, which is an extended family of models (kinetically roughened surfaces) which all share some non-Gaussian scaling limits and statistics, characterized by a few exponents different from the usual ones. Some other familiar members are some interacting particle systems (exclusion processes SSEP, ASEP, TASEP, q-TASEP), stochastic growth (random deposition, ballistic aggregation, polynuclear growth, Eden and Richardson model), first/last passage percolation, and some stochastic PDE’s (stochastic Burgers equation, stochastic reaction-diffusion equations, stochastic Hamilton-Jacobi equations). An elementary introduction [84] aiming at non-specialists mathematicians covers some of the above models, and can be completed by a more physics-oriented, but still pedestrian, account [155].