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arXiv · 1904.03319

The KPZ Universality Class and Related Topics

Axel Saenz
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Abstract

These notes are based on a talk given at the 2018 Arizona School of Analysis and Mathematical Physics. We give a comprehensive introduction to the KPZ universality class, a conjectured class of stochastic process with local interactions related to random growth processes in $1+1$ dimensions. We describe some of the characteristic properties of the KPZ universality class such as scaling exponents and limiting statistics. In particular, we aim to extract the characteristic properties of the KPZ universality class by understanding the KPZ stochastic partial differential equation by a special discrete approximation given by the asymmetric simple exclusion process (ASEP). The connection with the ASEP is very important as the process enjoys a rich integrability structure that leads to many exact formulas.

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Axel Saenz. 2019-04-05. The KPZ Universality Class and Related Topics. https://arxiv.org/abs/1904.03319

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