The Harmonic Descent Chain
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909195510480896 |
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| author | Aldous, David J. Janson, Svante Li, Xiaodan |
| author_facet | Aldous, David J. Janson, Svante Li, Xiaodan |
| contents | The decreasing Markov chain on \{1,2,3, \ldots\} with transition probabilities $p(j,j-i) \propto 1/i$ arises as a key component of the analysis of the beta-splitting random tree model. We give a direct and almost self-contained "probability" treatment of its occupation probabilities, as a counterpart to a more sophisticated but perhaps opaque derivation using a limit continuum tree structure and Mellin transforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Harmonic Descent Chain Aldous, David J. Janson, Svante Li, Xiaodan Probability 60J10 The decreasing Markov chain on \{1,2,3, \ldots\} with transition probabilities $p(j,j-i) \propto 1/i$ arises as a key component of the analysis of the beta-splitting random tree model. We give a direct and almost self-contained "probability" treatment of its occupation probabilities, as a counterpart to a more sophisticated but perhaps opaque derivation using a limit continuum tree structure and Mellin transforms. |
| title | The Harmonic Descent Chain |
| topic | Probability 60J10 |
| url | https://arxiv.org/abs/2405.05102 |