Localization over complex-analytic groupoids and conformal renormalization

We present a higher index theorem for a certain class of etale one-dimensional complex-analytic groupoids. The novelty is the use of the local anomaly formula established in a previous paper, which represents the bivariant Chern character of a quasihomomorphism as the chiral anomaly associated to a renormalized non-commutative chiral field theory. In the present situation the geometry is non-metric and the corresponding field theory can be renormalized in a purely conformal way, by exploiting the complex-analytic structure of the groupoid only. The index formula is automatically localized at the automorphism subset of the groupoid and involves a cap-product with the sum of two different cyclic cocycles over the groupoid algebra. The first cocycle is a trace involving a generalization of the Lefschetz numbers to higher-order fixed points. The second cocycle is a non-commutative Todd class, constructed from the modular automorphism group of the algebra.Comment: 38 pages. v2: some inconsistencies with the use of pseudogroups have been fixe

Convergence in law in the second Wiener/Wigner chaos

Let L be the class of limiting laws associated with sequences in the second Wiener chaos. We exhibit a large subset L_0 of L satisfying that, for any F_infinity in L_0, the convergence of only a finite number of cumulants suffices to imply the convergence in law of any sequence in the second Wiener chaos to F_infinity. This result is in the spirit of the seminal paper by Nualart and Peccati, in which the authors discovered the surprising fact that convergence in law for sequences of multiple Wiener-It\^o integrals to the Gaussian is equivalent to convergence of just the fourth cumulant. Also, we offer analogues of this result in the case of free Brownian motion and double Wigner integrals, in the context of free probability.Comment: 14 pages. This version corrects an error which, unfortunately, appears in the published version in EC

Random generation of finitely generated subgroups of a free group

We give an efficient algorithm to randomly generate finitely generated subgroups of a given size, in a finite rank free group. Here, the size of a subgroup is the number of vertices of its representation by a reduced graph such as can be obtained by the method of Stallings foldings. Our algorithm randomly generates a subgroup of a given size n, according to the uniform distribution over size n subgroups. In the process, we give estimates of the number of size n subgroups, of the average rank of size n subgroups, and of the proportion of such subgroups that have finite index. Our algorithm has average case complexity \O(n) in the RAM model and \O(n^2\log^2n) in the bitcost model

Scattering rates and lifetime of exact and boson excitons

Although excitons are not exact bosons, they are commonly treated as such provided that their composite nature is included in effective scatterings dressed by exchange. We here \emph{prove} that, \emph{whatever these scatterings are}, they cannot give both the scattering rates $T_{ij}^{-1}$ and the exciton lifetime $\tau_0$, correctly: A striking factor 1/2 exists between $\tau_0^{-1}$ and the sum of $T_{ij}^{-1}$'s, which originates from the composite nature of excitons, irretrievably lost when they are bosonized. This result, which appears as very disturbing at first, casts major doubts on bosonization for problems dealing with \emph{interacting} excitons

Size-assortative mating in simultaneous hermaphrodites: an experimental test and a meta-analysis

Assortative mating by size has been argued to be widespread in the animal kingdom. However, the strength of size-assortative mating is known to vary considerably between species and the underlying mechanisms promoting this inter-specific variation remain largely unexplored. Size-assortative mating has been proposed to be particularly strong in simultaneous hermaphrodites, i.e. organisms that produce male and female gametes at the same time. Here, we build on this hypothesis by arguing that size-assortative mating mediated by sexual selection is generally stronger in reciprocally mating hermaphrodites compared with unilaterally mating species and separate-sexed organisms. We report a series of empirical tests suggesting that size-assortative mating in the unilaterally copulating freshwater snail Physa acuta is caused by spatial clustering of similar-sized individuals and not by mate choice. In addition, we present a meta-analysis testing, for the first time, the hypothesis that sexual selection-mediated size-assortative mating is stronger in reciprocally copulating simultaneous hermaphrodites. Overall, we found significant size-assortative mating across 18 tested species and substantial inter-specific variation. Importantly, part of this variation can be explained by mating type, providing support for the hypothesis that size-assortative mating is stronger in reciprocally mating hermaphrodites compared with unilaterally mating species. We highlight potential pitfalls when testing for sexual selection-mediated size-assortative mating and discuss the need for more experimental and comparative approaches in order to resolve the observed variation in the strength of size-assortative mating among species.Fil: Graham, Stuart. Université de Montpellier. Centre d’Ecologie Fonctionnelle et Evolutive; Francia. Université Paul-Valéry Montpellier; Francia. Centre National de la Recherche Scientifique; FranciaFil: Chapuis, Elodie. Université de Montpellier. Centre d’Ecologie Fonctionnelle et Evolutive; Francia. Centre National de la Recherche Scientifique; Francia. Institut de Recherche pour le Développement,. Intéractions Plantes-Microrganismes-Environement; Francia. Université Paul-Valéry Montpellier; FranciaFil: Meconcelli, Stefania. Université de Montpellier. Centre d’Ecologie Fonctionnelle et Evolutive; Francia. Centre National de la Recherche Scientifique; Francia. Università di Torino; ItaliaFil: Bonel, Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Biología, Bioquímica y Farmacia. Laboratorio de Zoología de Invertebrados I; Argentina. Université de Montpellier. Centre d’Ecologie Fonctionnelle et Evolutive; Francia. Université Paul-Valéry Montpellier; FranciaFil: Sartori, Kevin. Université de Montpellier. Centre d’Ecologie Fonctionnelle et Evolutive; Francia. Centre National de la Recherche Scientifique; Francia. Université Paul-Valéry Montpellier; FranciaFil: Christophe, Ananda. Université de Montpellier. Centre d’Ecologie Fonctionnelle et Evolutive; Francia. Centre National de la Recherche Scientifique; Francia. Université Paul-Valéry Montpellier; FranciaFil: Alda, Maria del Pilar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Estudios Parasitológicos y de Vectores. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. Centro de Estudios Parasitológicos y de Vectores; ArgentinaFil: Patrice David. Université de Montpellier. Centre d’Ecologie Fonctionnelle et Evolutive; Francia. Centre National de la Recherche Scientifique; Francia. Université Paul-Valéry Montpellier; FranciaFil: Janicke, Tim. Université de Montpellier. Centre d’Ecologie Fonctionnelle et Evolutive; Francia. Centre National de la Recherche Scientifique; Francia. Université Paul-Valéry Montpellier; Franci

Processes with Long Memory: Regenerative Construction and Perfect Simulation

We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence. Even though the process has infinite memory, its value at time 0 depends only on a finite, but random, number of these uniform variables. The algorithm is based on a recent regenerative construction of these measures by Ferrari, Maass, Mart{\'\i}nez and Ney. As applications, we discuss the perfect simulation of binary autoregressions and Markov chains on the unit interval.Comment: 27 pages, one figure. Version accepted by Annals of Applied Probability. Small changes with respect to version

Theory of spin precession monitored by laser pulse

We first predict the splitting of a spin degenerate impurity level when this impurity is irradiated by a circularly polarized laser beam tuned in the transparency region of a semiconductor. This splitting, which comes from different exchange processes between the impurity electron and the virtual pairs coupled to the pump beam, induces a spin precession around the laser beam axis, which lasts as long as the pump pulse. It can thus be used for ultrafast spin manipulation. This effect, which has similarities with the exciton optical Stark effect we studied long ago, is here derived using the concepts we developed very recently to treat many-body interactions between composite excitons and which make the physics of this type of effects quite transparent. They, in particular, allow to easily extend this work to other experimental situations in which a spin rotates under laser irradiation.Comment: 12 pages + 1 figur

Conservation of geometric structures for non-homogeneous inviscid incompressible fluids

We obtain a result about propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension $N\geq2$. In particular, we investigate conservation of striated and conormal regularity, which is a natural way of generalizing the 2-D structure of vortex patches. The results we get are only local in time, even in the dimension N=2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N=2 or 3, we investigate also propagation of H\"older regularity in the interior of a bounded domain

One more approach to the convergence of the empirical process to the Brownian bridge

A theorem of Donsker asserts that the empirical process converges in distribution to the Brownian bridge. The aim of this paper is to provide a new and simple proof of this fact