25,506 research outputs found
Free products of sofic groups with amalgamation over monotileably amenable groups
We show that free products of sofic groups with amalgamation over
monotileably amenable subgroups are sofic. Consequently, so are HNN extensions
of sofic groups relative to homomorphisms of monotileably amenable subgroups.
We also show that families of independent uniformly distributed permutation
matrices and certain families of non-random permutation matrices (essentially,
those coming from quasi--actions of a sofic group) are asymptotically *-free as
the matrix size grows without bound.Comment: 16 pages. Version 2 has a shorter proof of Lemma 2.2, thanks to Ion
Nechita. Version 3 corrects a mistake. The previous Lemma 3.1 was incorrect.
Version 3 has a new proof of the main result, but it is (apparently) weaker
than in Version 2. Note that the paper's title also changed accordingly.
Version 4 corrects a minor mistake around equation (4
Groups acting on trees with almost prescribed local action
We investigate a family of groups acting on a regular tree, defined by
prescribing the local action almost everywhere. We study lattices in these
groups and give examples of compactly generated simple groups of finite
asymptotic dimension (actually one) not containing lattices. We also obtain
examples of simple groups with simple lattices, and we prove the existence of
(infinitely many) finitely generated simple groups of asymptotic dimension one.
We also prove various properties of these groups, including the existence of a
proper action on a CAT(0) cube complex.Comment: v2: 35 pages; argument slightly modified in 4.2.2; final versio
Random permutation matrices under the generalized Ewens measure
We consider a generalization of the Ewens measure for the symmetric group,
calculating moments of the characteristic polynomial and similar multiplicative
statistics. In addition, we study the asymptotic behavior of linear statistics
(such as the trace of a permutation matrix or of a wreath product) under this
new measure.Comment: Published in at http://dx.doi.org/10.1214/12-AAP862 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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