Author:
Dodos Pandelis,Tyros Konstantinos
Abstract
Abstract
Let A be a finite set with
, let n be a positive integer, and let
$A^n$
denote the discrete
$n\text {-dimensional}$
hypercube (that is,
$A^n$
is the Cartesian product of n many copies of A). Given a family
$\langle D_t:t\in A^n\rangle $
of measurable events in a probability space (a stochastic process), what structural information can be obtained assuming that the events
$\langle D_t:t\in A^n\rangle $
are not behaving as if they were independent? We obtain an answer to this problem (in a strong quantitative sense) subject to a mild ‘stationarity’ condition. Our result has a number of combinatorial consequences, including a new (and the most informative so far) proof of the density Hales-Jewett theorem.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献