Almost sure Assouad-like Dimensions of Complementary sets
Classical Analysis and ODEs
2019-03-20 v1 Metric Geometry
Probability
Abstract
Given a non-negative, decreasing sequence with sum , we consider all the closed subsets of such that the lengths of their complementary open intervals are given by the terms of , the so-called complementary sets. In this paper we determine the almost sure value of the -dimensions of these sets given a natural model of randomness. The -dimensions are intermediate Assouad-like dimensions which include the Assouad and quasi-Assouad dimensions as special cases. The answers depend on the size of , with one size behaving like the Assouad dimension and the other, like the quasi-Assouad dimension.
Cite
@article{arxiv.1903.07800,
title = {Almost sure Assouad-like Dimensions of Complementary sets},
author = {Ignacio García and Kathryn E. Hare and Franklin Mendivil},
journal= {arXiv preprint arXiv:1903.07800},
year = {2019}
}