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Alpha-stable random walk has massive thorns

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arxiv 1307.4947 v3 pith:KL3TJT4J submitted 2013-07-18 math.PR

Alexander Bendikov , Wojciech Cygan This is my paper · ORCID
classification math.PR
keywords massivemathbbalpharandomalpha-stableaxisclasscondition
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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 the thorn to be a massive set.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Bernstein Functions at Work: Coalescents, Copulas, and Subordination

    math.PR 2026-07 accept novelty 6.5 of 10

    Three open positivity problems on coalescent block counts, power-divergence copula generators, and special-Bernstein renewal sequences are resolved via Bernstein-function recognition calculus.

  2. The Logarithmic Laplacian on General Graphs

    math.AP 2025-07 conditional novelty 6.0 of 10

    The logarithmic Laplacian on weighted graphs is defined via a Bochner integral, given a kernel formula under stochastic completeness, and shown on Z^d to have sharp kernel bounds and exact diffusion asymptotics.

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