Universal aspects of curved, flat & stationary-state Kardar-Parisi-Zhang statistics
Abstract
Motivated by the recent exact solution of the stationary-state Kardar-Parisi-Zhang (KPZ) statistics by Imamura & 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.
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