A note on the asymptotics of the free energy of $1+1$ dimensional directed polymers in random environment at high temperature
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913759482609664 |
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| author | Nakashima, Makoto |
| author_facet | Nakashima, Makoto |
| contents | The author gave the sharp asymptotic behavior of the free energy of $1+1$ dimensional directed polymers in random environment(DPRE) as the inverse temperature $β\to 0$ under the assumption that random environment satisfies a certain concentration inequality in [Nak19], \[\lim_{β\to0}\frac{1}{β^4}F(β)=-\frac{1}{6}. \] In this paper, we obtain the same asymptotics without using the concentration inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the asymptotics of the free energy of $1+1$ dimensional directed polymers in random environment at high temperature Nakashima, Makoto Probability 82D60, 82C44 The author gave the sharp asymptotic behavior of the free energy of $1+1$ dimensional directed polymers in random environment(DPRE) as the inverse temperature $β\to 0$ under the assumption that random environment satisfies a certain concentration inequality in [Nak19], \[\lim_{β\to0}\frac{1}{β^4}F(β)=-\frac{1}{6}. \] In this paper, we obtain the same asymptotics without using the concentration inequality. |
| title | A note on the asymptotics of the free energy of $1+1$ dimensional directed polymers in random environment at high temperature |
| topic | Probability 82D60, 82C44 |
| url | https://arxiv.org/abs/2503.20192 |