The rank of sparse random matrices
Fuente:
arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866910494480138240 |
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| author | Coja-Oghlan, Amin Ergür, Alperen A. Gao, Pu Hetterich, Samuel Rolvien, Maurice |
| author_facet | Coja-Oghlan, Amin Ergür, Alperen A. Gao, Pu Hetterich, Samuel Rolvien, Maurice |
| contents | We determine the rank of a random matrix over an arbitrary field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula vindicates a conjecture of Lelarge (2013). The proofs are based on coupling arguments and a novel random perturbation, applicable to any matrix, that diminishes the number of short linear relations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_05757 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The rank of sparse random matrices Coja-Oghlan, Amin Ergür, Alperen A. Gao, Pu Hetterich, Samuel Rolvien, Maurice Combinatorics Discrete Mathematics Probability 05C80, 60B20, 94B05 We determine the rank of a random matrix over an arbitrary field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula vindicates a conjecture of Lelarge (2013). The proofs are based on coupling arguments and a novel random perturbation, applicable to any matrix, that diminishes the number of short linear relations. |
| title | The rank of sparse random matrices |
| topic | Combinatorics Discrete Mathematics Probability 05C80, 60B20, 94B05 |
| url | https://arxiv.org/abs/1906.05757 |