LDP for Inhomogeneous U-Statistics
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866908921999917056 |
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| author | Bhattacharya, Sohom Deb, Nabarun Mukherjee, Sumit |
| author_facet | Bhattacharya, Sohom Deb, Nabarun Mukherjee, Sumit |
| contents | In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a subgraph. We show that the corresponding rate functions in these cases can be expressed as a variational problem over a suitable space of functions. We use the tools developed to study Gibbs measures with the corresponding Hamiltonians, which include tensor generalizations of both Ising (with non-compact base measure) and Potts models. For these Gibbs measures, we establish scaling limits of log normalizing constants, and weak laws in terms of weak* topology, which are of possible independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_03944 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | LDP for Inhomogeneous U-Statistics Bhattacharya, Sohom Deb, Nabarun Mukherjee, Sumit Probability Mathematical Physics Statistics Theory 60F10, 05C80, 82B20 In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a subgraph. We show that the corresponding rate functions in these cases can be expressed as a variational problem over a suitable space of functions. We use the tools developed to study Gibbs measures with the corresponding Hamiltonians, which include tensor generalizations of both Ising (with non-compact base measure) and Potts models. For these Gibbs measures, we establish scaling limits of log normalizing constants, and weak laws in terms of weak* topology, which are of possible independent interest. |
| title | LDP for Inhomogeneous U-Statistics |
| topic | Probability Mathematical Physics Statistics Theory 60F10, 05C80, 82B20 |
| url | https://arxiv.org/abs/2212.03944 |