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Weak and strong moments of random vectors

Rafał Latała (2011)

Banach Center Publications

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.

Weak Distances between Random Subproportional Quotients of ℓ ₁ m

Piotr Mankiewicz (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

Lower estimates for weak distances between finite-dimensional Banach spaces of the same dimension are investigated. It is proved that the weak distance between a random pair of n-dimensional quotients of ℓ ₁ n ² is greater than or equal to c√(n/log³n).

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