Number of arithmetic progressions in dense random subsets of ℤ/nℤ

Autor:	Mehtaab Sawhney, Ashwin Sah, Ross Berkowitz
Rok vydání:	2021
Předmět:	Set (abstract data type) Degree (graph theory) Distribution (number theory) General Mathematics Basis function Arithmetic Element (category theory) Constant (mathematics) Random variable Central limit theorem Mathematics
Zdroj:	Israel Journal of Mathematics. 244:589-620
ISSN:	1565-8511 0021-2172
Popis:	We examine the behavior of the number of k-term arithmetic progressions in a random subset of ℤ/nℤ. We prove that if a set is chosen by including each element of ℤ/nℤ independently with constant probability p, then the resulting distribution of k-term arithmetic progressions in that set, while obeying a central limit theorem, does not obey a local central limit theorem. The methods involve decomposing the random variable into homogeneous degree d polynomials with respect to the Walsh/Fourier basis. Proving a suitable multivariate central limit theorem for each component of the expansion gives the desired result.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::04df5239d7ea6a66d26075057fda5e52 https://doi.org/10.1007/s11856-021-2180-7 Zobrazit plný text záznamu Full text from SpringerLink