Volume growth and heat kernel estimates for the continuum random tree
Volume growth and heat kernel estimates for the continuum random tree
复制标题
连续随机树的体积增长和热核估计
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
D. Croydon
中科院分区：
文献类型：
--
作者：
D. Croydon
在这篇文章中，我们证明了连续随机树的整体和局部（逐点）体积和热核界。我们证明了当r → 0时，半径为r的球的体积关于首阶多项式项存在几乎必然的对数全局涨落和对数对数局部涨落。我们还证明了当t → 0时，热核的对角部分几乎必然表现出相应的全局和局部涨落.最后，我们证明，这种淬火（几乎肯定）的行为与当地退火（平均在所有实现的树）的体积和热核的行为，这是顺利的。
In this article, we prove global and local (point-wise) volume and heat kernel bounds for the continuum random tree. We demonstrate that there are almost–surely logarithmic global fluctuations and log–logarithmic local fluctuations in the volume of balls of radius r about the leading order polynomial term as r → 0. We also show that the on-diagonal part of the heat kernel exhibits corresponding global and local fluctuations as t → 0 almost–surely. Finally, we prove that this quenched (almost–sure) behaviour contrasts with the local annealed (averaged over all realisations of the tree) volume and heat kernel behaviour, which is smooth.