Geodesic
$\alpha $-stable random walk has massive thorns
Alexander Bendikov 1   ; Wojciech Cygan 1
1 Institute of Mathematics Wrocław University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
Colloquium Mathematicum, Tome 138 (2015) no. 1, pp. 105-129 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm138-1-7
Keywords: introduce study class random walks defined integer lattice mathbb discrete space time counterpart symmetric alpha stable process mathbb alpha coordinate axis mathbb geq non massive set whereas cone massive provide necessary sufficient condition thorn massive set

Alexander Bendikov  1   ; Wojciech Cygan  1

1 Institute of Mathematics Wrocław University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland 
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Alexander Bendikov; Wojciech Cygan. $\alpha $-stable random walk has massive thorns. Colloquium Mathematicum, Tome 138 (2015) no. 1, pp. 105-129. doi: 10.4064/cm138-1-7

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