Motivated by the recent exact solution of the stationary-state Kardar-Parisi-Zhang (KPZ) statistics by Imamura and Sasamoto [Phys. Rev. Lett. 108, 190603 (2012)], as well as a precursor experimental signature unearthed by Takeuchi [Phys. Rev. Lett. 110, 210604 (2013)], we establish here the universality of these phenomena, examining scaling behaviors of directed polymers in a random medium, the stochastic heat equation with multiplicative noise, and kinetically roughened KPZ growth models. We emphasize the value of cross KPZ-class universalities, revealing crossover effects of experimental relevance. Finally, we illustrate the great utility of KPZ scaling theory by an optimized numerical analysis of the Ulam problem of random permutations.

• Received 23 October 2013

DOI:https://doi.org/10.1103/PhysRevE.89.010103