We prove small-deviation estimates for the volume of random convex sets. The focus is on convex hulls and Minkowski sums of line segments generated by independent random points. The random models considered include (Lebesgue) absolutely continuous probability measures with bounded densities and the class of log-concave measures.

We model the development of the linear complexity of multisequences by a stochastic infinite state machine, the Battery–Discharge– Model, BDM. The states s ∈ S of the BDM have asymptotic probabilities or mass μ∞(s) = P(q,M) −1 ·q−K(s), whereK(s) ∈ N0 is the class of the state s, and P(q,M) = ∑ K∈N0 PM (K)q −K = ∏M i=1 q i/(qi − 1) is the generating function of the number of partitions into at m...

We present a deterministic algorithm running in space O ? log 2 n= log logn solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(logn) time-bounded algorithm for this problem running on a parallel pointer machine.

Let X=(X(t))t ¥ T be a symmetric a-stable, 0 < a < 2, process with paths in the dual Eg of a certain Banach space E. Then there exists a (bounded, linear) operator u from E into some La(S, s) generating X in a canonical way. The aim of this paper is to compare the degree of compactness of u with the small deviation (ball) behavior of f(e)=−log P(||X||E* < e) as eQ 0. In particular, we prove tha...