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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.01348 |
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| _version_ | 1866929300030095360 |
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| author | Aldous, David J. Feng, Shi |
| author_facet | Aldous, David J. Feng, Shi |
| contents | Consider a compact metric space $S$ and a pair $(j,k)$ with $k \ge 2$ and $1 \le j \le k$. For any probability distribution $θ\in P(S)$, define a Markov chain on $S$ by: from state $s$, take $k$ i.i.d. ($θ$) samples, and jump to the $j$'th closest. Such a chain converges in distribution to a unique stationary distribution, say $π_{j,k}(θ)$. So this defines a mapping $π_{j,k}: P(S) \to P(S)$. What happens when we iterate this mapping? In particular, what are the fixed points of this mapping? We present a few rigorous results, to complement our extensive simulation study elsewhere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Markov chains and mappings of distributions on compact spaces Aldous, David J. Feng, Shi Probability Metric Geometry 60J05 Consider a compact metric space $S$ and a pair $(j,k)$ with $k \ge 2$ and $1 \le j \le k$. For any probability distribution $θ\in P(S)$, define a Markov chain on $S$ by: from state $s$, take $k$ i.i.d. ($θ$) samples, and jump to the $j$'th closest. Such a chain converges in distribution to a unique stationary distribution, say $π_{j,k}(θ)$. So this defines a mapping $π_{j,k}: P(S) \to P(S)$. What happens when we iterate this mapping? In particular, what are the fixed points of this mapping? We present a few rigorous results, to complement our extensive simulation study elsewhere. |
| title | Markov chains and mappings of distributions on compact spaces |
| topic | Probability Metric Geometry 60J05 |
| url | https://arxiv.org/abs/2404.01348 |