title: Universal aspects of curved, flat, and stationary-state Kardar-Parisi-Zhang statistics.
abstract: 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.
authors.affiliation: Physics Department, Barnard College, Columbia University, New York, New York 10027, USA.
authors.forename: Timothy
authors.initials: T
authors.lastname: Halpin-Healy
authors.affiliation: Physics Department, Barnard College, Columbia University, New York, New York 10027, USA.
authors.forename: Yuexia
authors.initials: Y
authors.lastname: Lin