arXiv subjects

Yutaka Takeuchi

Publications and source records attributed to Yutaka Takeuchi.

3 recordsLinked to original sources

arXiv2024

Subcritical regimes in the Poisson Boolean percolation on Ahlfors regular spaces

The Poisson Boolean percolation on a metric measure space is one of the percolation models. Intuitively, this model is obtained by collecting random balls whose centers form a Poisson point process. In 2008, Gou\'{e}r\'{e} proved that for $n \geq 2$, the Poisson Boolean percolation on $\mathbb{R}^n$ has the subcritical regime if and only if the radius distribution has finite $n$-th moment. In this paper, we extend Gou\'{e}r\'{e}'s result to Ahlfors regular metric measure spaces.

math.PR↗

arXiv2023

Local Central Limit Theorem for Reflecting Diffusions in a Continuum Percolation Cluster

Reflecting diffusions on continuum percolation clusters are considered. Assuming that the occupied region has a unique unbounded cluster and the cluster satisfies geometrical conditions such as volume regularity, isoperimetric conditions, and a hole size condition, we prove a quenched local central limit theorem for reflecting diffusions on the cluster.

math.PR↗

arXiv2022

Quenched Invariance Principle for a Reflecting Diffusion in a Continuum Percolation Cluster

We consider a continuum percolation built over stationary ergodic point processes. Assuming that the occupied region has a unique unbounded cluster and the cluster satisfies volume regularity and isoperimetric condition, we prove a quenched invariance principle for reflecting diffusions on the cluster.

math.PR↗