Non-Gibbsian Multivariate Ewens Probability Distributions on Regular Trees
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916614028394496 |
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| author | Haydarov, F. H. Mustafoyeva, Z. E. Rozikov, U. A. |
| author_facet | Haydarov, F. H. Mustafoyeva, Z. E. Rozikov, U. A. |
| contents | Ewens' sampling formula (ESF) provides the probability distribution governing the number of distinct genetic types and their respective frequencies at a selectively neutral locus under the infinitely-many-alleles model of mutation. A natural and significant question arises: ``Is the Ewens probability distribution on regular trees Gibbsian?"
In this paper, we demonstrate that Ewens probability distributions can be regarded as non-Gibbsian distributions on regular trees and derive a sufficient condition for the consistency condition. This study lays the groundwork for a new direction in the theory of non-Gibbsian probability distributions on trees. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_10114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Gibbsian Multivariate Ewens Probability Distributions on Regular Trees Haydarov, F. H. Mustafoyeva, Z. E. Rozikov, U. A. Probability Functional Analysis 60K35 Ewens' sampling formula (ESF) provides the probability distribution governing the number of distinct genetic types and their respective frequencies at a selectively neutral locus under the infinitely-many-alleles model of mutation. A natural and significant question arises: ``Is the Ewens probability distribution on regular trees Gibbsian?" In this paper, we demonstrate that Ewens probability distributions can be regarded as non-Gibbsian distributions on regular trees and derive a sufficient condition for the consistency condition. This study lays the groundwork for a new direction in the theory of non-Gibbsian probability distributions on trees. |
| title | Non-Gibbsian Multivariate Ewens Probability Distributions on Regular Trees |
| topic | Probability Functional Analysis 60K35 |
| url | https://arxiv.org/abs/2502.10114 |