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Updated: May 2, 2026

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Published on: June 8, 2018
Universal aspects of curved, flat, and stationary-state Kardar-Parisi-Zhang statistics
Timothy Halpin-Healy1, Yuexia Lin1
1Physics Department, Barnard College, Columbia University, New York, New York 10027, USA.
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.
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