arXiv subjects
Publications and source records attributed to Stiene Riemer.
Given an Orlicz function $M$, we show which random variables $ξ_i$, $i=1,...,n$ generate the associated Orlicz norm, i.e., which random variables yield $\mathbb{E} \max\limits_{1\leq i \leq n}|x_iξ_i| \sim \norm{(x_i)_{i=1}^n}_M$. As a corollary we obtain a representation for the distribution function in terms of $M$ and $M'$ which can be easily applied to many examples of interest.
We give estimates for the expectation of the norm of random matrices with independent but not necessarily identically distributed entries.
Let $ξ_i$, $i=1,...,n$, and $η_j$, $j=1,...,m$ be iid p-stable respectively q-stable random variables, $1<p<q<2$. We prove estimates for $\Ex_{Ω_1} \Ex_{Ω_2}\max_{i,j}\abs{a_{ij}ξ_i(ω_1)η_j(ω_2)}$ in terms of the $\ell_p^m(\ell_q^n)$-norm of $(a_{ij})_{i,j}$. Additionally, for p-stable and standard gaussian random variables we prove estimates in terms of the $\ell_p^m(\ell_{M_ξ}^n)$-norm, $M_ξ$ depending on the Gaussians. Furthermore, we show that a sequence $ξ_i$, $i=1,...,n$ of iid $\log-γ(1,p)$ distributed random variables ($p\geq 2$) generates a truncated $\ell_p$-norm, especially $\Ex \max_{i}\abs{a_iξ_i}\sim \norm{(a_i)_i}_2$ for $p=2$. As far as we know, the generating distribution for $\ell_p$-norms with $p\geq 2$ has not been known up to now.