Convergence of dynamical stationary fluctuations
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915195601813504 |
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| author | Labbé, Cyril Laslier, Benoît Toninelli, Fabio Zambotti, Lorenzo |
| author_facet | Labbé, Cyril Laslier, Benoît Toninelli, Fabio Zambotti, Lorenzo |
| contents | We present a general black box theorem that ensures convergence of a sequence of stationary Markov processes, provided a few assumptions are satisfied. This theorem relies on a control of the resolvents of the sequence of Markov processes, and on a suitable characterization of the resolvents of the limit. One major advantage of this approach is that it circumvents the use of the Boltzmann-Gibbs principle: for instance, we deduce in a rather simple way that the stationary fluctuations of the one-dimensional zero-range process converge to the stochastic heat equation. More importantly, it allows to establish results that were probably out of reach of existing methods: using the black box result, we are able to prove that the stationary fluctuations of a discrete model of ordered interfaces, that was considered previously in the statistical physics literature, converge to a system of reflected stochastic PDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18803 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence of dynamical stationary fluctuations Labbé, Cyril Laslier, Benoît Toninelli, Fabio Zambotti, Lorenzo Probability Mathematical Physics We present a general black box theorem that ensures convergence of a sequence of stationary Markov processes, provided a few assumptions are satisfied. This theorem relies on a control of the resolvents of the sequence of Markov processes, and on a suitable characterization of the resolvents of the limit. One major advantage of this approach is that it circumvents the use of the Boltzmann-Gibbs principle: for instance, we deduce in a rather simple way that the stationary fluctuations of the one-dimensional zero-range process converge to the stochastic heat equation. More importantly, it allows to establish results that were probably out of reach of existing methods: using the black box result, we are able to prove that the stationary fluctuations of a discrete model of ordered interfaces, that was considered previously in the statistical physics literature, converge to a system of reflected stochastic PDEs. |
| title | Convergence of dynamical stationary fluctuations |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2404.18803 |