Abstract:Let $\{X_n= e^{2\pi i \theta_n}\}$ be a sequence of Steinhaus random variables, where $\theta_n$ are independent and uniformly distributed on $[0,1]$. We compute the almost sure Hausdorff dimension of the images and graphs of the random complex series $S(x)=\sum_{n=1}^{\infty}a_n X_n\phi_n(\lambda_nx)$, where $\lambda_n$ is an increasing sequence with $\sup_n\lambda_{n+1}/\lambda_n<\infty$ and $\phi_n$ satisfies some uniform Lipschitz and boundedness conditions. This class of series includes the famous Weierstrass and Riemann functions as well as others appeared in literature. These results help predict the exact values of the deterministic cases.
From: Peng-Fei Zhang [view email]
[v1]
Fri, 6 Mar 2026 07:38:43 UTC (3,654 KB)
[v2]
Thu, 3 Sep 2026 09:26:26 UTC (3,655 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。