On the joint distribution of the area and the number of peaks for Bernoulli excursions
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913628817457152 |
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| author | Kargin, Vladislav |
| author_facet | Kargin, Vladislav |
| contents | Let $P_n$ be a random Bernoulli excursion of length $2n$. We show that the area under $P_n$ and the number of peaks of $P_n$ are asymptotically independent. We also show that these statistics have the correlation coefficient asymptotic to $c /\sqrt{n}$ for large $n$, where $c < 0$, and explicitly compute the coefficient $c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the joint distribution of the area and the number of peaks for Bernoulli excursions Kargin, Vladislav Probability Combinatorics Let $P_n$ be a random Bernoulli excursion of length $2n$. We show that the area under $P_n$ and the number of peaks of $P_n$ are asymptotically independent. We also show that these statistics have the correlation coefficient asymptotic to $c /\sqrt{n}$ for large $n$, where $c < 0$, and explicitly compute the coefficient $c$. |
| title | On the joint distribution of the area and the number of peaks for Bernoulli excursions |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2412.20315 |