A factorization formula for the partition function in the semi-discrete parabolic Anderson model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913107945717760 |
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| author | Hurth, Tobias Khanin, Konstantin Lameda, Beatriz Navarro |
| author_facet | Hurth, Tobias Khanin, Konstantin Lameda, Beatriz Navarro |
| contents | We consider a continuous-time simple symmetric random walk on the integer lattice $\mathbb{Z}^d$ in dimension $d \geq 3$, subject to a random potential given by a field of two-sided Wiener processes. In the high-temperature regime, we prove the existence of the $L^2$- and almost sure limits of the partition function as time $t \to \pm \infty$, and show that these limiting partition functions are positive almost surely. Our main result is a factorization formula for the point-to-point partition function, which is shown to be valid up to any sub-ballistic scale. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_09377 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A factorization formula for the partition function in the semi-discrete parabolic Anderson model Hurth, Tobias Khanin, Konstantin Lameda, Beatriz Navarro Probability Dynamical Systems 60H15, 35R60, 37L40, 60K35, 60F05 We consider a continuous-time simple symmetric random walk on the integer lattice $\mathbb{Z}^d$ in dimension $d \geq 3$, subject to a random potential given by a field of two-sided Wiener processes. In the high-temperature regime, we prove the existence of the $L^2$- and almost sure limits of the partition function as time $t \to \pm \infty$, and show that these limiting partition functions are positive almost surely. Our main result is a factorization formula for the point-to-point partition function, which is shown to be valid up to any sub-ballistic scale. |
| title | A factorization formula for the partition function in the semi-discrete parabolic Anderson model |
| topic | Probability Dynamical Systems 60H15, 35R60, 37L40, 60K35, 60F05 |
| url | https://arxiv.org/abs/2605.09377 |