Concentration of norms of random vectors with independent p-sub-exponential coordinates

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 Lᵖ L p -norms of these p -norms of random vectors. In the first case p≥ 1 p ≥ 1 , our estimates depend on the dimension n of random vectors. But in the second one for p≥ 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.