Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/31899
Title: Limit theorems for a class of unbounded observables with an application to ‘Sampling the Lindelöf hypothesis’
Authors: Fernando, K
Schindler, TI
Keywords: central limit theorem;Edgeworth expansion;unbounded observables;Lindelöf hypothesis;quasicompact transfer operators
Issue Date: 12-Aug-2025
Publisher: Cambridge University Press (CUP)
Citation: Fernando, K. and Schindler, T.I. (2025) 'Limit theorems for a class of unbounded observables with an application to ‘Sampling the Lindelöf hypothesis’', Ergodic Theory and Dynamical Systems,0 (ahead of print), pp. 1 - 59. doi: 10.1017/etds.2025.10203.
Abstract: We prove the central limit theorem (CLT), the first-order Edgeworth expansion and a mixing local central limit theorem (MLCLT) for Birkhoff sums of a class of unbounded heavily oscillating observables over a family of full-branch piecewise C^2 expanding maps of the interval. As a corollary, we obtain the corresponding results for Boolean-type transformations on \mathbb {R}. The class of observables in the CLT and the MLCLT on \mathbb {R} include the real part, the imaginary part and the absolute value of the Riemann zeta function. Thus obtained CLT and MLCLT for the Riemann zeta function are in the spirit of the results of Lifschitz & Weber [Sampling the Lindelöf hypothesis with the Cauchy random walk. Proc. Lond. Math. Soc. (3) 98 (2009), 241–270] and Steuding [Sampling the Lindelöf hypothesis with an ergodic transformation. RIMS Kôkyûroku Bessatsu B34 (2012), 361–381] who have proven the strong law of large numbers for sampling the Lindelöf hypothesis.
Description: MSC classification: Primary: 37A50: Relations with probability theory and stochastic processes Secondary: 60F05: Central limit and other weak theorems 11M06: zeta(s) and L(s,chi)
URI: https://bura.brunel.ac.uk/handle/2438/31899
DOI: https://doi.org/10.1017/etds.2025.10203
ISSN: 0143-3857
Other Identifiers: ORCiD: Kasun Fernando https://orcid.org/0000-0003-1489-9566
ORCiD: Tanka I. Schindler https://orcid.org/0000-0002-9056-8884
Appears in Collections:Dept of Mathematics Research Papers

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