Year: 2025
Type: article
Abstract: We present examples of p -sub-exponential random variables for any positive p . We prove two types of concentration of standard p -norms (2-norm is the Euclidean norm) of random vectors with independent p -sub-exponential coordinates around the Lebesgue $$L^p$$ L p -norms of these p -norms of random vectors. In the first case $$p\ge 1$$ p ≥ 1 , our estimates depend on the dimension n of random vectors. But in the second one for $$p\ge 2$$ p ≥ 2 , with an additional assumption, we get an estimate that does not depend on n . In other words, we generalize some known concentration results in the Euclidean case to cases of the p -norms of random vectors with independent p -sub-exponential coordinates.
Source: Archiv der Mathematik
Author: Krzysztof Zajkowski
Institution: University of Białystok
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4416772180