How large should be the redundant numbers of copy to make a rare event probable
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866910545794301952 |
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| author | Paquin-Lefebvre, Fred Toste, Suney Holcman, David |
| author_facet | Paquin-Lefebvre, Fred Toste, Suney Holcman, David |
| contents | The redundancy principle provides the framework to study how rare events are made possible with probability 1 in accelerated time, by making many copies of similar random searchers. But what is $n$ large? To estimate large $n$ with respect to the geometrical properties of a domain and the dynamics, we present here a criteria based on splitting probabilities between a small fraction of the exploration space associated to an activation process and other absorbing regions where trajectories can be terminated. We obtain explicit computations especially when there is a killing region located inside the domain that we compare with stochastic simulations. We present also examples of extreme trajectories with killing in dimension 2. For a large $n$, the optimal trajectories avoid penetrating inside the killing region. Finally we discuss some applications to cell biology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12687 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | How large should be the redundant numbers of copy to make a rare event probable Paquin-Lefebvre, Fred Toste, Suney Holcman, David Soft Condensed Matter Analysis of PDEs Quantitative Methods The redundancy principle provides the framework to study how rare events are made possible with probability 1 in accelerated time, by making many copies of similar random searchers. But what is $n$ large? To estimate large $n$ with respect to the geometrical properties of a domain and the dynamics, we present here a criteria based on splitting probabilities between a small fraction of the exploration space associated to an activation process and other absorbing regions where trajectories can be terminated. We obtain explicit computations especially when there is a killing region located inside the domain that we compare with stochastic simulations. We present also examples of extreme trajectories with killing in dimension 2. For a large $n$, the optimal trajectories avoid penetrating inside the killing region. Finally we discuss some applications to cell biology. |
| title | How large should be the redundant numbers of copy to make a rare event probable |
| topic | Soft Condensed Matter Analysis of PDEs Quantitative Methods |
| url | https://arxiv.org/abs/2206.12687 |