@article{1fe889e5dc854e3383dae4d7821bc815,

title = "LOWER TAILS VIA RELATIVE ENTROPY",

abstract = "We show that the naive mean-field approximation correctly predicts the leading term of the logarithmic lower tail probabilities for the number of copies of a given subgraph in G(n,p) and of arithmetic progressions of a given length in random subsets of the integers in the entire range of densities where the mean-field approximation is viable. Our main technical result provides sufficient conditions on the maximum degrees of a uniform hypergraph H that guarantee that the logarithmic lower tail probabilities for the number of edges, induced by a binomial random subset of the vertices of H, can be well approximated by considering only product distributions. This may be interpreted as a weak, probabilistic version of the hypergraph container lemma that is applicable to all sparser-than-average (and not only independent) sets.",

keywords = "Lower tail, random graph, subgraph counts",

author = "Gady Kozma and Wojciech Samotij",

note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2023",

year = "2023",

doi = "10.1214/22-AOP1610",

language = "אנגלית",

volume = "51",

pages = "665--698",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

number = "2",

}