论文标题
在某些自符号分形和Weyl的特征值的laplacian：对成真的理论方面的调查
The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: A survey of the ergodic-theoretic aspects
论文作者
论文摘要
这项简短的调查旨在勾勒出作者最近关于Weyl的特征值渐近学研究的千古来理论方面。通过将Kesten的更新定理[\ emph {Ann。\ prob。} \ \ \\ textbf {2}（1974），355---386，定理2]用于Markov链上的一般状态空间上的功能，并提供了替代概率的概率，并提供了由OH OH [ \ textbf {187}（2012），1--35，推论1.8]在阿波罗尼亚垫圈中圆圈的渐近分布。
This short survey is aimed at sketching the ergodic-theoretic aspects of the author's recent studies on Weyl's eigenvalue asymptotics for a \emph{"geometrically canonical" Laplacian} defined by the author on some self-conformal circle packing fractals including the classical \emph{Apollonian gasket}. The main result being surveyed is obtained by applying Kesten's renewal theorem [\emph{Ann.\ Probab.}\ \textbf{2} (1974), 355--386, Theorem 2] for functionals of Markov chains on general state spaces and provides an alternative probabilistic proof of the result by Oh and Shah [\emph{Invent.\ Math.}\ \textbf{187} (2012), 1--35, Corollary 1.8] on the asymptotic distribution of the circles in the Apollonian gasket.
