Alpha-stable random walk has massive thorns
Alexander Bendikov, Wojciech Cygan

TL;DR
This paper introduces a class of discrete alpha-stable random walks on integer lattices, analyzing conditions under which certain subsets like axes and cones are massive or non-massive, extending continuous stable process theory.
Contribution
It establishes a discrete analogue of symmetric alpha-stable processes and characterizes the massiveness of thorn sets in higher dimensions.
Findings
Axes are non-massive sets for 0<α<2 in dimensions d≥3.
Any cone is a massive set under the same conditions.
Provides necessary and sufficient conditions for thorn sets to be massive.
Abstract
We introduce and study a class of random walks defined on the integer lattice -- a discrete space and time counterpart of the symmetric -stable process in . When any coordinate axis in , , is a non-massive set whereas any cone is massive. We provide a necessary and sufficient condition for the thorn to be a massive set.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
