28,900 research outputs found
Singularity analysis, Hadamard products, and tree recurrences
We present a toolbox for extracting asymptotic information on the
coefficients of combinatorial generating functions. This toolbox notably
includes a treatment of the effect of Hadamard products on singularities in the
context of the complex Tauberian technique known as singularity analysis. As a
consequence, it becomes possible to unify the analysis of a number of
divide-and-conquer algorithms, or equivalently random tree models, including
several classical methods for sorting, searching, and dynamically managing
equivalence relationsComment: 47 pages. Submitted for publicatio
A Note on trapped Surfaces in the Vaidya Solution
The Vaidya solution describes the gravitational collapse of a finite shell of
incoherent radiation falling into flat spacetime and giving rise to a
Schwarzschild black hole. There has been a question whether closed trapped
surfaces can extend into the flat region (whereas closed outer trapped surfaces
certainly can). For the special case of self-similar collapse we show that the
answer is yes, if and only if the mass function rises fast enough.Comment: 14 pages, 4 figures; minor polish added to version
The Tensor Track, III
We provide an informal up-to-date review of the tensor track approach to
quantum gravity. In a long introduction we describe in simple terms the
motivations for this approach. Then the many recent advances are summarized,
with emphasis on some points (Gromov-Hausdorff limit, Loop vertex expansion,
Osterwalder-Schrader positivity...) which, while important for the tensor track
program, are not detailed in the usual quantum gravity literature. We list open
questions in the conclusion and provide a rather extended bibliography.Comment: 53 pages, 6 figure
Acoustics of early universe. I. Flat versus open universe models
A simple perturbation description unique for all signs of curvature, and
based on the gauge-invariant formalisms is proposed to demonstrate that:
(1) The density perturbations propagate in the flat radiation-dominated
universe in exactly the same way as electromagnetic or gravitational waves
propagate in the epoch of the matter domination.
(2) In the open universe, sounds are dispersed by curvature. The space
curvature defines the minimal frequency below which the
propagation of perturbations is forbidden.
Gaussian acoustic fields are considered and the curvature imprint in the
perturbations spectrum is discussed.Comment: The new version extended by 2 sections. Changes in notation. Some
important comments adde
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