The main objective of this survey is to present thestate of the art'of those parts of the theory of
independent functions which are related to the geometry of function spaces. Thesize'of a …

For a given sequence of real numbers $ a_ {1},\dots, a_ {n} $, we denote the $ k $ th
smallest one by ${k\mbox {-}\min} _ {1\leq i\leq n} a_ {i} $. Let $\mathcal {A} $ be a class of …

We prove sharp bounds for the expectation of the supremum of the Gaussian process
indexed by the intersection of Bpn with ρBqn for 1⩽ p, q⩽∞ and ρ> 0, and by the …

Let X_i,j, i,j=1,...,n, be independent, not necessarily identically distributed random variables
with finite first moments. We show that the norm of the random matrix (X_i,j)_i,j=1^n is up to a …

On the Expectation of Operator Norms of Random Matrices | SpringerLink Skip to main content
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Let 1⩽ p< 2 and let L p= L p [0, 1] be the classical L p-space of all (classes of) p-integrable
functions on [0, 1]. It is known that any subspace in L p spanned by a sequence of …

We study geometric parameters associated with the Banach spaces (R n,‖·‖ k, q) normed
by‖ x‖ k, q=(∑ 1⩽ i⩽ k|〈 x, ai〉|∗ q) 1/q, where {ai} i⩽ N is a given sequence of N points in …

Abstract Let X 1, X 2,…, X n be a sequence of independent random variables, let M be a
rearrangement invariant space on the underlying probability space, and let N be a …

Let F be a class of functions on a probability space (Ω, μ) and let X 1,..., X k be independent
random variables distributed according to μ. We establish an upper bound that holds with …

We prove two-sided Chevet-type inequalities for independent symmetric Weibull random
variables with shape parameter $ r\in [1, 2] $. We apply them to provide two-sided estimates …