Year: 2023
Type: preprint
Abstract: We consider the distribution of the binomial probability mass function (pmf) among arithmetic progressions and obtain an average-type theorem. As applications, we consider the possible visits to a kind of sieved sets of integers or lattice points, by an $α$-random walker. We show that, almost surely, the asymptotic proportion of time the random walker in a sieved set of the type is equal to the density of the set, independently of $α$.
Source: arXiv (Cornell University)
Authors: Hong, Jun, Wu, Xiaosheng, Zhu, Shixin
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4383604725