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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2502.04113 |
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| _version_ | 1866917407480610816 |
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| author | Junk, Stefan Lacoin, Hubert |
| author_facet | Junk, Stefan Lacoin, Hubert |
| contents | For the directed polymer in a random environment (DPRE), two critical inverse-temperatures can be defined. The first one, $β_c$, separates the strong disorder regime (in which the normalized partition function $W^β_n$ tends to zero) from the weak disorder regime (in which $W^β_n$ converges to a nontrivial limit). The other, $\bar β_c$, delimits the very strong disorder regime (in which $W^β_n$ converges to zero exponentially fast). It was proved previously that $β_c=\bar β_c$ when the random environment is upper-bounded for the DPRE based on the simple random walk. We extend this result to general environment and arbitrary reference walk. We also prove that $β_c=0$ if and only the $L^2$-critical point is trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04113 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coincidence of critical points for directed polymers for general environments and random walks Junk, Stefan Lacoin, Hubert Probability For the directed polymer in a random environment (DPRE), two critical inverse-temperatures can be defined. The first one, $β_c$, separates the strong disorder regime (in which the normalized partition function $W^β_n$ tends to zero) from the weak disorder regime (in which $W^β_n$ converges to a nontrivial limit). The other, $\bar β_c$, delimits the very strong disorder regime (in which $W^β_n$ converges to zero exponentially fast). It was proved previously that $β_c=\bar β_c$ when the random environment is upper-bounded for the DPRE based on the simple random walk. We extend this result to general environment and arbitrary reference walk. We also prove that $β_c=0$ if and only the $L^2$-critical point is trivial. |
| title | Coincidence of critical points for directed polymers for general environments and random walks |
| topic | Probability |
| url | https://arxiv.org/abs/2502.04113 |