Large deviations for multiple ergodic averages. Issue 8 (17th November 2017)

• Record Type: Journal Article
• Authors: Mesón, Alejandro; Vericat, Fernando
• Is Part Of: Journal of interdisciplinary mathematics. Volume 20:Issue 8(2017)
• Page Start: 1603
• Page End: 1617
• Publication Date: 2017-11-17
• Subjects: 37C45 -- 37B40; Large deviations -- multiple ergodic average; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.1080/09720502.2018.1423910
• Languages: English
• ISSNs: 0972-0502

Abstract

Abstract: The main purpose of this work is to estimate how multiple ergodic averages appart from a given quantity. This problem can be studied by describing a large deviation process for empirical measures as obtained by using the contraction principle. The case of single ergodic averages for empirical measures was already studied by Pfister and Sullivan [Nonlinarity, 10 (2005) 237-261]. To have a more complete picture on empirical measures and V – statistics, we estimate the size of the sets GK = { x : Lr ( x ) ⊂ K }, where Lr ( x ) is the limit-point set of the sequence of empirical measures and K is a compact subset of ℳ(X r ) with ℳ(X) the set of measures on X . In pasrticular, we obtain a variational formula for the topological entropy of Gk . The result of this work about the dimension of the sets Gk can be compared with the one recently circulated by Fan, Schemeling and Wu [arXiv:1206.3214v1 (2012)].