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)}.
A Local Limit Theorem for Cliques in G(n,p)
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
citation-role summary
method 1
citation-polarity summary
fields
math.CO 1years
2019 1verdicts
ACCEPT 1roles
method 1polarities
use method 1representative citing papers
citing papers explorer
-
An algebraic inverse theorem for the quadratic Littlewood-Offord problem, and an application to Ramsey graphs
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)}.