Metastability of Glauber dynamics with inhomogeneous coupling disorder
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866913422070775808 |
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| author | Bovier, Anton Hollander, Frank den Marello, Saeda Pulvirenti, Elena Slowik, Martin |
| author_facet | Bovier, Anton Hollander, Frank den Marello, Saeda Pulvirenti, Elena Slowik, Martin |
| contents | We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates of metastability in large volumes at fixed temperatures when these systems evolve according to a Glauber dynamics, i.e.\ where spins flip with Metropolis transition probabilities at inverse temperature $β$. We identify conditions ensuring that with high probability the system behaves like the corresponding system where the random couplings are replaced by their averages. More precisely, we prove that the metastability of the former system is implied with high probability by the metastability of the latter. Moreover, we consider relevant metastable hitting times of the two systems and find the asymptotic tail behaviour and the moments of their ratio. This work provides an extension of the results known for the Ising model on the Erdős--R{é}nyi random graph. The proofs use the potential-theoretic approach to metastability in combination with concentration inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_09827 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Metastability of Glauber dynamics with inhomogeneous coupling disorder Bovier, Anton Hollander, Frank den Marello, Saeda Pulvirenti, Elena Slowik, Martin Probability 60K35, 60K37, 82B20, 82B44, 82C44 We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates of metastability in large volumes at fixed temperatures when these systems evolve according to a Glauber dynamics, i.e.\ where spins flip with Metropolis transition probabilities at inverse temperature $β$. We identify conditions ensuring that with high probability the system behaves like the corresponding system where the random couplings are replaced by their averages. More precisely, we prove that the metastability of the former system is implied with high probability by the metastability of the latter. Moreover, we consider relevant metastable hitting times of the two systems and find the asymptotic tail behaviour and the moments of their ratio. This work provides an extension of the results known for the Ising model on the Erdős--R{é}nyi random graph. The proofs use the potential-theoretic approach to metastability in combination with concentration inequalities. |
| title | Metastability of Glauber dynamics with inhomogeneous coupling disorder |
| topic | Probability 60K35, 60K37, 82B20, 82B44, 82C44 |
| url | https://arxiv.org/abs/2209.09827 |