Random $p$-adic Riesz products: Continuity, singularity, and dimension
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- Proc. Amer. Math. Soc. 137 (2009), 3477-3486 Request permission
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 $p^{-k}$.References
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Additional Information
- Narn-Rueih Shieh
- Affiliation: Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan
- Email: shiehnr@math.ntu.edu.tw
- Xiong-ying Zhang
- Affiliation: Department of Mathematics, South China University of Technology, 510640 Guangzhou, People’s Republic of China
- Email: xiongyzh@scut.edu.cn
- Received by editor(s): June 9, 2008
- Published electronically: June 3, 2009
- Communicated by: Richard C. Bradley
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3477-3486
- MSC (2000): Primary 60G57, 28A80, 11S80
- DOI: https://doi.org/10.1090/S0002-9939-09-09991-2
- MathSciNet review: 2515417