Large deviation principles for graphon sampling
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913808830693376 |
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| author | Grebík, Jan Pikhurko, Oleg |
| author_facet | Grebík, Jan Pikhurko, Oleg |
| contents | We investigate possible large deviation principles (LDPs) for the $n$-vertex sampling from a given graphon with various speeds $s(n)$ and resolve all the cases except when the speed $s(n)$ is of order $n^2$.
For quadratic speed $s=(c+o(1))n^2$, we establish an LDP for an arbitrary $k$-step graphon, which extends a result of Chatterjee and Varadhan [Europ. J. Combin., 32 (2011) 1000-1017] who did this for $k=1$ (that is, for the homogeneous binomial random graphs). This is done by reducing the problem to the LDP for stochastic $k$-block models established recently by Borgs, Chayes, Gaudio, Petti and Sen ["A large deviation principle for block models", arxiv:2007.14508, 2020]. Also, we improve some results by Borgs et al. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_06531 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Large deviation principles for graphon sampling Grebík, Jan Pikhurko, Oleg Probability Combinatorics We investigate possible large deviation principles (LDPs) for the $n$-vertex sampling from a given graphon with various speeds $s(n)$ and resolve all the cases except when the speed $s(n)$ is of order $n^2$. For quadratic speed $s=(c+o(1))n^2$, we establish an LDP for an arbitrary $k$-step graphon, which extends a result of Chatterjee and Varadhan [Europ. J. Combin., 32 (2011) 1000-1017] who did this for $k=1$ (that is, for the homogeneous binomial random graphs). This is done by reducing the problem to the LDP for stochastic $k$-block models established recently by Borgs, Chayes, Gaudio, Petti and Sen ["A large deviation principle for block models", arxiv:2007.14508, 2020]. Also, we improve some results by Borgs et al. |
| title | Large deviation principles for graphon sampling |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2311.06531 |