Pith. sign in

REVIEW 1 cited by

A Local Limit Theorem for Cliques in G(n,p)

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1811.03527 v1 pith:QNX5KWHY submitted 2018-11-08 math.CO

classification math.CO
keywords characteristiccliquesfunctionlimitlocalrandomtheoremaccomplished
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We prove a local limit theorem the number of $r$-cliques in $G(n,p)$ for $p\in(0,1)$ and $r\ge 3$ fixed constants. Our bounds hold in both the $\ell^\infty$ and $\ell^1$ metric. The main work of the paper is an estimate for the characteristic function of this random variable. This is accomplished by introducing a new technique for bounding the characteristic function of constant degree polynomials in independent Bernoulli random variables, combined with a decoupling argument.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An algebraic inverse theorem for the quadratic Littlewood-Offord problem, and an application to Ramsey graphs

    math.CO 2019-09 accept novelty 8.0 of 10

    If a quadratic Bernoulli polynomial has a point probability much larger than 1/n, it is close to a quadratic form of low rank; a consequence bounds edge-count point probabilities in Ramsey graphs by n^{-1+o(1)}.

Pith tools