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α-stable random walk has massive thorns

Alexander Bendikov, Wojciech Cygan (2015)

Colloquium Mathematicae

We introduce and study a class of random walks defined on the integer lattice d -a discrete space and time counterpart of the symmetric α-stable process in d . When 0 < α <2 any coordinate axis in d , d ≥ 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.

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