Galton, Matt (2019) Limit theorems for slowly mixing dynamical systems. PhD thesis, University of Warwick.

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Abstract

In this thesis we prove the iterated weak invariance principle for ergodic, probability-preserving dynamical systems with respect to L∞ observables under a mild mixing assumption. When the dynamics can be modelled by a Young tower the iterated weak invariance principle is already known under optimal conditions. The setting where T is not necessarily modelled by a Young tower still has gaps, however. This is the setup considered in this thesis, and it is flexible enough to include time-one maps of suitable (semi-)flows. For both non-invertible and invertible maps, we improve upon the previous best results. For non-invertible maps, our mixing assumption is optimal when correlations decay at polynomial rates.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Differentiable dynamical systems, Ergodic Theory
Official Date:	2019
Dates:	Date Event 2019 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Melbourne, Ian
Format of File:	pdf
Extent:	vi, 85 leaves : illustrations
Language:	eng

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