Self-repellent branching random walk
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911509900165120 |
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| author | Bovier, Anton Hartung, Lisa Hollander, Frank den |
| author_facet | Bovier, Anton Hartung, Lisa Hollander, Frank den |
| contents | We consider a system of particles performing a discrete-time binary branching random walk with independent standard normal increments subject to a penalty $\b$ for every pair of particles that get within distance $\e$ of each other at every time. We study the optimal configurations that minimise the sum of the spread out cost and the repulsion cost up to a given time horizon $N$. We show that at time $N$ particles are spread out over a distance $\asymp (\b\e)^{1/3} 2^{2N/3}$. We also show that the total cost of the optimal configurations up to time $N$ is $\asymp (\b\e)^{2/3} 2^{4N/3}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-repellent branching random walk Bovier, Anton Hartung, Lisa Hollander, Frank den Probability Statistical Mechanics Mathematical Physics 60J80, 60G70, 82B44 We consider a system of particles performing a discrete-time binary branching random walk with independent standard normal increments subject to a penalty $\b$ for every pair of particles that get within distance $\e$ of each other at every time. We study the optimal configurations that minimise the sum of the spread out cost and the repulsion cost up to a given time horizon $N$. We show that at time $N$ particles are spread out over a distance $\asymp (\b\e)^{1/3} 2^{2N/3}$. We also show that the total cost of the optimal configurations up to time $N$ is $\asymp (\b\e)^{2/3} 2^{4N/3}$. |
| title | Self-repellent branching random walk |
| topic | Probability Statistical Mechanics Mathematical Physics 60J80, 60G70, 82B44 |
| url | https://arxiv.org/abs/2407.15533 |