An appetizer to modern developments on the Kardar–Parisi–Zhang universality class

By K. Takeuchi. Physica A: Statistical Mechanics and its Applications, 2017

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Abstract The Kardar–Parisi–Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few. Since the year 2000, our understanding of the one-dimensional KPZ class has been completely renewed by mathematical physics approaches based on exact solutions. Mathematical physics has played a central role since then, leading to a myriad of new developments, but their implications are clearly not limited to mathematics — as a matter of fact, it can also be studied experimentally. The aim of these lecture notes is to provide an introduction to the field that is accessible to non-specialists, reviewing basic properties of the KPZ class and highlighting main physical outcomes of mathematical developments since the year 2000. It is written in a brief and self-contained manner, with emphasis put on physical intuitions and implications, while only a small (and mostly not the latest) fraction of mathematical developments could be covered. Liquid-crystal experiments by the author and coworkers are also reviewed.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cb82f40a30a547d0d6921916bfdd1948d34fe094

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The directed landscape (2018, background): “e introduction suitable for a newcomer to the area, see Romik (2015). Review articles and books focusing on more recent developments include Corwin 8 (2016), Ferrari and Spohn (2010), Quastel (2011), Takeuchi (2018) and Weiss, Ferrari and Spohn (2017). The Baik, Deift and Johansson (1999) proof for ”