Large Deviations of First Passage Times of Branching Random Walks in $\mathbb{R}^d$: Asymptotics and Algorithms
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913998011629568 |
|---|---|
| author | Blanchet, Jose Cai, Wei Mohanty, Shaswat Zhang, Zhenyuan |
| author_facet | Blanchet, Jose Cai, Wei Mohanty, Shaswat Zhang, Zhenyuan |
| contents | We investigate the large deviation probabilities of first passage times (FPT) of discrete-time supercritical non-lattice branching random walks (BRWs) in $\mathbb{R}^d$ where $d\geq 1$. The FPT refers to the first time the BRW enters a ball of radius one with a distance $x$ from the origin, conditioned upon the process's survival. Furthermore, we apply the spine decomposition technique to construct an asymptotically optimal polynomial-time algorithm for computing the lower large deviation probabilities of the FPT. The accuracy of our algorithm is also verified numerically. Our analysis not only provides a deeper theoretical understanding of these stochastic processes but also offers new insights into the microstructural features that are key to characterizing the strength of polymers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large Deviations of First Passage Times of Branching Random Walks in $\mathbb{R}^d$: Asymptotics and Algorithms Blanchet, Jose Cai, Wei Mohanty, Shaswat Zhang, Zhenyuan Probability We investigate the large deviation probabilities of first passage times (FPT) of discrete-time supercritical non-lattice branching random walks (BRWs) in $\mathbb{R}^d$ where $d\geq 1$. The FPT refers to the first time the BRW enters a ball of radius one with a distance $x$ from the origin, conditioned upon the process's survival. Furthermore, we apply the spine decomposition technique to construct an asymptotically optimal polynomial-time algorithm for computing the lower large deviation probabilities of the FPT. The accuracy of our algorithm is also verified numerically. Our analysis not only provides a deeper theoretical understanding of these stochastic processes but also offers new insights into the microstructural features that are key to characterizing the strength of polymers. |
| title | Large Deviations of First Passage Times of Branching Random Walks in $\mathbb{R}^d$: Asymptotics and Algorithms |
| topic | Probability |
| url | https://arxiv.org/abs/2506.15072 |