When Janson meets McDiarmid: Bounded difference inequalities under graph-dependence

Zhang, Rui-Ray

doi:10.1016/j.spl.2021.109272

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Cluster Expansion and Dependency Graphs1

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2022

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“…(see, for example, [7,8]). They are also heavily used in probabilistic combinatorics, such as Lovász local lemma [3], Janson's inequality [9], concentration inequalities [21], etc.…”

Section: Cluster Expansion and Dependency Graphsmentioning

confidence: 99%

Asymptotic linearity of binomial random hypergraphs via cluster expansion under graph-dependence

Zhang¹

2022

Preprint

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Let integer n3 and integer r = r(n) 3. Define the binomial random r-uniform hypergraph H r (n, p) to be the r-uniform graph on the vertex set [n] such that each rset is an edge independently with probability p. A hypergraph is linear if every pair of hyperedges intersects in at most one vertex. We study the probability of linearity of random hypergraphs H r (n, p) via cluster expansion and give more precise asymptotics of the probability in question, improving the asymptotic probability of linearity obtained by McKay and Tian, in particular, when r = 3 and p = o(n −7/5 ).

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“…(see, for example, [7,8]). They are also heavily used in probabilistic combinatorics, such as Lovász local lemma [3], Janson's inequality [9], concentration inequalities [21], etc.…”

Section: Cluster Expansion and Dependency Graphsmentioning

confidence: 99%

Asymptotic linearity of binomial random hypergraphs via cluster expansion under graph-dependence

Zhang¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Asymptotic linearity of binomial random hypergraphs via cluster expansion under graph-dependence

Zhang

2022

Advances in Applied Mathematics

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When Janson meets McDiarmid: Bounded difference inequalities under graph-dependence

Cited by 2 publications

References 13 publications

Asymptotic linearity of binomial random hypergraphs via cluster expansion under graph-dependence

Asymptotic linearity of binomial random hypergraphs via cluster expansion under graph-dependence

Asymptotic linearity of binomial random hypergraphs via cluster expansion under graph-dependence

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