## Tokyo Journal of Mathematics

### Heat Kernel Estimates for Random Walks on Some Kinds of One-dimensional Continuum Percolation Clusters

Jun MISUMI

#### Abstract

We consider random walks on random graphs determined by a some kind of continuum percolation on $\mathbf{R}$. The vertex set of the random graph is given by the Poisson points conditioned that all points of $\mathbf{Z}$ are contained. The edge set of the random graph is determined by the random radii of the spheres centered at each points. We give heat kernel estimates for the random walks under the condition on the moment of the random radii. We will also discuss random walks on continuum percolation clusters in $\mathbf{R}^d$, $d\ge 2$.

#### Article information

Source
Tokyo J. Math., Volume 34, Number 1 (2011), 1-17.

Dates
First available in Project Euclid: 11 August 2011

https://projecteuclid.org/euclid.tjm/1313074443

Digital Object Identifier
doi:10.3836/tjm/1313074443

Mathematical Reviews number (MathSciNet)
MR2866635

Zentralblatt MATH identifier
1235.60140

#### Citation

MISUMI, Jun. Heat Kernel Estimates for Random Walks on Some Kinds of One-dimensional Continuum Percolation Clusters. Tokyo J. Math. 34 (2011), no. 1, 1--17. doi:10.3836/tjm/1313074443. https://projecteuclid.org/euclid.tjm/1313074443

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