On massive sets for subordinated random walks |
| |
| Authors: | Alexander Bendikov Wojciech Cygan |
| |
| Affiliation: | 1. +48 71 375 7476+48 71 375 7401;2. Institute of Mathematics, Wroclaw University, Wroclaw, Poland |
| |
| Abstract: | We study massive (reccurent) sets with respect to a certain random walk  defined on the integer lattice  ,  . Our random walk  is obtained from the simple random walk S on  by the procedure of discrete subordination.  can be regarded as a discrete space and time counterpart of the symmetric α‐stable Lévy process in  . In the case  we show that some remarkable proper subsets of  , e.g. the set  of primes, are massive whereas some proper subsets of  such as the Leitmann primes  are massive/non‐massive depending on the function h. Our results can be regarded as an extension of the results of McKean (1961) about massiveness of the set of primes for the simple random walk in  . In the case  we study massiveness of thorns and their proper subsets. The case  is presented in the recent paper Bendikov and Cygan 2 . |
| |
| Keywords: | Capacity Green function random walk regular variation subordination 31A15 05C81 60J45 |
|
|
