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Random $ p$-adic Riesz products: Continuity, singularity, and dimension

Authors: Narn-Rueih Shieh and Xiong-ying Zhang
Journal: Proc. Amer. Math. Soc. 137 (2009), 3477-3486
MSC (2000): Primary 60G57, 28A80, 11S80
Published electronically: June 3, 2009
MathSciNet review: 2515417
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Abstract: We study precise conditions for mutual absolute continuity and mutual singularity of two random $ p$-adic Riesz products, defined respectively by two sequences of coefficients $ a_k, b_k$. Our conditions and assertions are specific to the $ p$-adic case. We also calculate explicitly the Hausdorff dimension, and in case the defining coefficients are constant, we have an integral representation of the dimension formula with a rapid convergence rate $ p^{-k}$.

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Additional Information

Narn-Rueih Shieh
Affiliation: Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan

Xiong-ying Zhang
Affiliation: Department of Mathematics, South China University of Technology, 510640 Guangzhou, People’s Republic of China

Keywords: Random $p$-adic Riesz products, mutual absolute continuity, mutual singularity, Hausdorff dimension
Received by editor(s): June 9, 2008
Published electronically: June 3, 2009
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.