$\alpha $-stable random walk has massive thorns
Volume 138 / 2015
Colloquium Mathematicum 138 (2015), 105-129
MSC: 60G50, 31B15.
DOI: 10.4064/cm138-1-7
Abstract
We introduce and study a class of random walks defined on the integer lattice $\mathbb {Z} ^d$—a discrete space and time counterpart of the symmetric $\alpha $-stable process in $\mathbb {R} ^d$. When $0< \alpha <2$ any coordinate axis in $\mathbb {Z} ^d$, $d\geq 3$, is a non-massive set whereas any cone is massive. We provide a necessary and sufficient condition for a thorn to be a massive set.
