Weak and strong moments of random vectors
Rafa{\l} Lata{\l}a
TL;DR
This paper investigates the relationship between weak and strong moments of log-concave random vectors, proving a key inequality for unconditional vectors in certain normed spaces.
Contribution
It establishes the conjectured inequality for unconditional vectors in normed spaces with bounded cotype, advancing understanding of moment comparisons.
Findings
Proves the inequality for unconditional vectors in specific normed spaces.
Supports the conjecture relating weak and strong moments of log-concave vectors.
Provides new bounds in the context of cotype constants.
Abstract
We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant.
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