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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.10320 |
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| _version_ | 1866915858527289344 |
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| author | Athreya, Siva Joseph, Mathew Mueller, Carl |
| author_facet | Athreya, Siva Joseph, Mathew Mueller, Carl |
| contents | In [AJM26], we gave large-time asymptotic bounds on the annealed survival probability of a moving polymer taking values in ${\mathbb R}^d, d \geq 1$. This polymer is a solution of a stochastic heat equation driven by additive spacetime white noise on $[0,T] \times [0,J]$, in an environment of Poisson traps. For fixed $J$, the annealed survivial probability decays exponentially with rate proportional to $T^{d/(d+2)}$. In this work we examine the large $J$ asymptotics of the annealed survival probability for any fixed time $T>0$. We prove upper and lower bounds for the annealed survival probability in the cases of hard obstacles. Our bounds decay exponentially with rate proportional to $J^{d/(d+2)}$. The exponents also depend on time $T >0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10320 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Survival of a long random string among hard Poisson traps Athreya, Siva Joseph, Mathew Mueller, Carl Probability 60H15, 60G17, 60G60 In [AJM26], we gave large-time asymptotic bounds on the annealed survival probability of a moving polymer taking values in ${\mathbb R}^d, d \geq 1$. This polymer is a solution of a stochastic heat equation driven by additive spacetime white noise on $[0,T] \times [0,J]$, in an environment of Poisson traps. For fixed $J$, the annealed survivial probability decays exponentially with rate proportional to $T^{d/(d+2)}$. In this work we examine the large $J$ asymptotics of the annealed survival probability for any fixed time $T>0$. We prove upper and lower bounds for the annealed survival probability in the cases of hard obstacles. Our bounds decay exponentially with rate proportional to $J^{d/(d+2)}$. The exponents also depend on time $T >0$. |
| title | Survival of a long random string among hard Poisson traps |
| topic | Probability 60H15, 60G17, 60G60 |
| url | https://arxiv.org/abs/2603.10320 |