6,387 research outputs found

    Higher cyclic operads

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    We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category Ξ\Xi of trees, which carries a tight relationship to the Moerdijk-Weiss category of rooted trees Ω\Omega. We prove a nerve theorem exhibiting colored cyclic operads as presheaves on Ξ\Xi 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

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    We prove that the diffusion coefficient for the asymmetric exclusion process diverges at least as fast as t1/4t^{1/4} in dimension d=1d=1 and (logt)1/2(\log t)^{1/2} in d=2d=2. The method applies to nearest and non-nearest neighbor asymmetric exclusion processes

    Hom-quantum groups I: quasi-triangular Hom-bialgebras

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    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

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    An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.Comment: 10 pages. To appear in Communications in Algebr

    Transient analysis of synchronous machines.

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    Zooming in on local level statistics by supersymmetric extension of free probability

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    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

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    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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