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arXiv · 2401.15016

KPZ fluctuations in finite volume

Sylvain Prolhac
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Abstract

These lecture notes, adapted from the habilitation thesis of the author, survey in a first part various exact results obtained in the past few decades about KPZ fluctuations in one dimension, with a special focus on finite volume effects describing the relaxation to its stationary state of a finite system starting from a given initial condition. The second part is more specifically devoted to an approach allowing to express in a simple way the statistics of the current in the totally asymmetric simple exclusion process in terms of a contour integral on a compact Riemann surface, whose infinite genus limit leads to KPZ fluctuations in finite volume.

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Sylvain Prolhac. 2024-01-26. KPZ fluctuations in finite volume. https://doi.org/10.21468/scipostphyslectnotes.81

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