KPZ fluctuations in finite volume
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866929381486624768 |
|---|---|
| author | Prolhac, Sylvain |
| author_facet | Prolhac, Sylvain |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | KPZ fluctuations in finite volume Prolhac, Sylvain Probability Statistical Mechanics Mathematical Physics 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. |
| title | KPZ fluctuations in finite volume |
| topic | Probability Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2401.15016 |