5,671 research outputs found
On the permanent of random Bernoulli matrices
We show that the permanent of an matrix with iid Bernoulli
entries is of magnitude with probability .
In particular, it is almost surely non-zero
Central limit theorems for Gaussian polytopes
Choose random, independent points in according to the standard
normal distribution. Their convex hull is the {\sl Gaussian random
polytope}. We prove that the volume and the number of faces of satisfy
the central limit theorem, settling a well known conjecture in the field.Comment: to appear in Annals of Probabilit
The Topology of Foliations Formed by the Generic K-Orbits of a Subclass of the Indecomposable MD5-Groups
The present paper is a continuation of [13], [14] of the authors.
Specifically, the paper considers the MD5-foliations associated to connected
and simply connected MD5-groups such that their Lie algebras have 4-dimensional
commutative derived ideal. In the paper, we give the topological classification
of all considered MD5-foliations. A description of these foliations by certain
fibrations or suitable actions of and the Connes' C*-algebras
of the foliations which come from fibrations are also given in the paper.Comment: 20 pages, no figur
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