6,388 research outputs found
Higher cyclic operads
We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category of trees, which carries a tight relationship to the Moerdijk-Weiss category of rooted trees . We prove a nerve theorem exhibiting colored cyclic operads as presheaves on which satisfy a Segal condition. Finally, we produce a Quillen model category whose fibrant objects satisfy a weak Segal condition, and we consider these objects as an up-to-homotopy generalization of the concept of cyclic operad
Superdiffusivity of asymmetric exclusion process in dimensions one and two
We prove that the diffusion coefficient for the asymmetric exclusion process
diverges at least as fast as in dimension and
in . The method applies to nearest and non-nearest neighbor asymmetric
exclusion processes
Hom-quantum groups I: quasi-triangular Hom-bialgebras
We introduce a Hom-type generalization of quantum groups, called
quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative
analogues of Drinfel'd's quasi-triangular bialgebras, in which the
non-(co)associativity is controlled by a twisting map. A family of
quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular
bialgebra, such as Drinfel'd's quantum enveloping algebras. Each
quasi-triangular Hom-bialgebra comes with a solution of the quantum
Hom-Yang-Baxter equation, which is a non-associative version of the quantum
Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained
from modules of suitable quasi-triangular Hom-bialgebras.Comment: 21 page
Deformation of dual Leibniz algebra morphisms
An algebraic deformation theory of morphisms of dual Leibniz algebras is
obtained.Comment: 10 pages. To appear in Communications in Algebr
Zooming in on local level statistics by supersymmetric extension of free probability
We consider unitary ensembles of Hermitian NxN matrices H with a confining
potential NV where V is analytic and uniformly convex. From work by
Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit
of the characteristic function for a finite-rank Fourier variable K is
determined by the Voiculescu R-transform, a key object in free probability
theory. Going beyond these results, we argue that the same holds true when the
finite-rank operator K has the form that is required by the Wegner-Efetov
supersymmetry method of integration over commuting and anti-commuting
variables. This insight leads to a potent new technique for the study of local
statistics, e.g., level correlations. We illustrate the new technique by
demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section
Topological Censorship
All three-manifolds are known to occur as Cauchy surfaces of asymptotically
flat vacuum spacetimes and of spacetimes with positive-energy sources. We prove
here the conjecture that general relativity does not allow an observer to probe
the topology of spacetime: any topological structure collapses too quickly to
allow light to traverse it. More precisely, in a globally hyperbolic,
asymptotically flat spacetime satisfying the null energy condition, every
causal curve from \scri^- to {\scri}^+ is homotopic to a topologically
trivial curve from \scri^- to {\scri}^+. (If the Poincar\'e conjecture is
false, the theorem does not prevent one from probing fake 3-spheres).Comment: 12 pages, REVTEX; 1 postscript figure in a separate uuencoded file.
Our earlier version (PRL 71, 1486 (1993)) contained a secondary result,
mistakenly attributed to Schoen and Yau, regarding ``passive topological
censorship'' of a certain class of topologies. As Gregory Burnett has pointed
out (gr-qc/9504012), this secondary result is false. The main topological
censorship theorem is unaffected by the erro
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