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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.02562 |
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Table of 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.