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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2402.02562 |
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| _version_ | 1866917069843333120 |
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| author | Junk, Stefan Lacoin, Hubert |
| author_facet | Junk, Stefan Lacoin, Hubert |
| contents | We show that if the normalized partition function $W^β_n$ of the directed polymer model on $\mathbb Z^d$ converges to zero, then it does so exponentially fast. This implies that there exists a critical value $β_c$ for the inverse temperature such that the normalized partition function has a non-degenerate limit for all $β\in [0,β_c]$ -- weak disorder holds -- while for $β\in (β_c,\infty)$ it converges exponentially fast to zero -- very strong disorder holds. This solves a twenty-years-old conjecture formulated by Comets, Yoshida, Carmona and Hu. Our proof requires a technical assumption on the environment, namely, that it is bounded from above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02562 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong disorder and very strong disorder are equivalent for directed polymers Junk, Stefan Lacoin, Hubert Probability Mathematical Physics We show that if the normalized partition function $W^β_n$ of the directed polymer model on $\mathbb Z^d$ converges to zero, then it does so exponentially fast. This implies that there exists a critical value $β_c$ for the inverse temperature such that the normalized partition function has a non-degenerate limit for all $β\in [0,β_c]$ -- weak disorder holds -- while for $β\in (β_c,\infty)$ it converges exponentially fast to zero -- very strong disorder holds. This solves a twenty-years-old conjecture formulated by Comets, Yoshida, Carmona and Hu. Our proof requires a technical assumption on the environment, namely, that it is bounded from above. |
| title | Strong disorder and very strong disorder are equivalent for directed polymers |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2402.02562 |