报告人：任浩杰 博士后 （以色列理工学院）

时间：2024年12月06日 15:30-

腾讯会议ID: 123-233-349

会议链接：https://meeting.tencent.com/dm/EdcvjXVY6Md1 

摘要：For \((\lambda_1, \ldots, \lambda_d) = \lambda \in (0,1)^d\) with \(\lambda_1 > \ldots > \lambda_d\), the Bernoulli convolution \(\mu_\lambda\) is the distribution of \(\sum_{n \geq 0} \pm (\lambda_1^n, \ldots, \lambda_d^n)\), where the \(\pm\) signs are independent and equally likely. Assuming no \(\lambda_j\) is a root of a polynomial with coefficients in \(\{\pm 1, 0\}\), we prove \(\dim(\mu_\lambda) = \min\{\dim_L(\mu_\lambda), d\}\), where \(\dim_L\) is the Lyapunov dimension.

This generalizes to homogeneous diagonal self-affine systems on \(\mathbb{R}^d\) with rational translations, extending results by Breuillard and Varjú. A key novelty is an explicit higher-dimensional entropy increase result. Joint work with Ariel Rapaport.

邀请人: 数学研究中心

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