ETDs @PUC-Rio
| Título: | ARITHMETIC STRUCTURES IN RANDOM SETS | ||||||||||||
| Autor: |
MATHEUS SECCO TORRES DA SILVA |
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| Colaborador(es): |
SIMON RICHARD GRIFFITHS - Orientador |
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| Catalogação: | 08/SET/2020 | Língua(s): | ENGLISH - UNITED STATES |
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| Tipo: | TEXT | Subtipo: | THESIS | ||||||||||
| Notas: |
[pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio. [en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio. |
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| Referência(s): |
[pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=49323&idi=1 [en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=49323&idi=2 |
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| DOI: | https://doi.org/10.17771/PUCRio.acad.49323 | ||||||||||||
| Resumo: | |||||||||||||
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In this Ph.D. thesis, we study bounds for the deviation probabilities of a random variable X that counts the number of edges of a hypergraph induced by a random m–element subset of its vertex set. We consider two contexts: the first corresponds to hypergraphs with some kind of regularity, whereas the second addresses hypergraphs that are in some sense far from being regular. It is possible to apply these results to discrete structures such as the set of k–term arithmetic progressions in the additive group of integers modulo a prime and in the set of the first N positive integers. Furthermore, we also deduce results for the case when the random subset is generated by including each vertex of the hypergraph independently with probability p.
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