%0 Journal Article
%T Probabilistic regularity lemma and its applications in combinatorics
%A Bosni£¿
%A Filip
%A Kova£¿
%A Vjekoslav
%J -
%D 2017
%X Sa£¿etak This paper begins with two well-known theorems from additive combinatorics, which are then reduced to a result from graph theory. A further generalization is formulated in the language of probability theory, in order to be established using the probabilistic variant of the Szemer¨¦di regularity lemma. This lemma provides a decomposition of an arbitrary random variable into a structured part, a pseudorandom part, and an error, and the paper presents its complete proof
%K arithmetic progression
%K Roth¡¯s theorem
%K corner
%K undirected graph
%K pseudorandomness
%K conditional expectation
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=271512