KPZ fluctuations in the planar stochastic heat equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909775007055872 |
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| author | Quastel, Jeremy Ramirez, Alejandro Virag, Balint |
| author_facet | Quastel, Jeremy Ramirez, Alejandro Virag, Balint |
| contents | We use a version of the Skorokhod integral to give a simple and rigorous formulation of the Wick-ordered (stochastic) heat equation with planar white noise, representing the free energy of an undirected random polymer. The solution for all times is expressed as the L1 limit of a martingale given by the Feyman-Kac formula and defines a randomized shift, or Gaussian multiplicative chaos. The fluctuations far from the centre are shown to be given by the one-dimensional KPZ equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13607 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | KPZ fluctuations in the planar stochastic heat equation Quastel, Jeremy Ramirez, Alejandro Virag, Balint Probability Mathematical Physics Analysis of PDEs We use a version of the Skorokhod integral to give a simple and rigorous formulation of the Wick-ordered (stochastic) heat equation with planar white noise, representing the free energy of an undirected random polymer. The solution for all times is expressed as the L1 limit of a martingale given by the Feyman-Kac formula and defines a randomized shift, or Gaussian multiplicative chaos. The fluctuations far from the centre are shown to be given by the one-dimensional KPZ equation. |
| title | KPZ fluctuations in the planar stochastic heat equation |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2210.13607 |