Asympotic behavior of the total length of external branches for Beta-coalescents

We consider a ${\Lambda}$-coalescent and we study the asymptotic behavior of the total length $L^{(n)}_{ext}$ of the external branches of the associated $n$-coalescent. For Kingman coalescent, i.e. ${\Lambda}={\delta}_0$, the result is well known and is useful, together with the total length $L^{(n)}$, for Fu and Li's test of neutrality of mutations% under the infinite sites model asumption . For a large family of measures ${\Lambda}$, including Beta$(2-{\alpha},{\alpha})$ with $0<\alpha<1$, M{\"o}hle has proved asymptotics of $L^{(n)}_{ext}$. Here we consider the case when the measure ${\Lambda}$ is Beta$(2-{\alpha},{\alpha})$, with $1<\alpha<2$. We prove that $n^{{\alpha}-2}L^{(n)}_{ext}$ converges in $L^2$ to $\alpha(\alpha-1)\Gamma(\alpha)$. As a consequence, we get that $L^{(n)}_{ext}/L^{(n)}$ converges in probability to $2-\alpha$. To prove the asymptotics of $L^{(n)}_{ext}$, we use a recursive construction of the $n$-coalescent by adding individuals one by one. Asymptotics of the distribution of $d$ normalized external branch lengths and a related moment result are also given

Persistent Currents and Magnetization in two-dimensional Magnetic Quantum Systems

Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the ``classical'' relationship between current and magnetization is shown to hold for systems invariant both by translation and rotation. Applications are given, including the point vortex superposed to an homogeneous magnetic field, the quantum Hall geometry (an electric field and an homogeneous magnetic field) and the random magnetic impurity problem (a random distribution of point vortices).Comment: 27 pages latex, 1 figur

An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations

For monotone linear differential systems with periodic coefficients, the (first) Floquet eigenvalue measures the growth rate of the system. We define an appropriate arithmetico-geometric time average of the coefficients for which we can prove that the Perron eigenvalue is smaller than the Floquet eigenvalue. We apply this method to Partial Differential Equations, and we use it for an age-structured systems of equations for the cell cycle. This opposition between Floquet and Perron eigenvalues models the loss of circadian rhythms by cancer cells.Comment: 7 pages, in English, with an abridged French versio

Empirical Comparisons of In-Store Display vs. Feature Advertising and Trade Promotions vs. Consumer Promotions, Measured at the Brand and the Category Levels

Marketing,

Why economic growth dynamics matter inassessing climate change damages: illustrationon extreme events

Extreme events are one of the main channels through which climate and socio- economic systems interact and it is likely that climate change will modify their probability distributions. The long-term growth models used in climate change as- sessments, however, cannot capture the effects of such short-term shocks. To inves- tigate this issue, a non-equilibrium dynamic model (NEDyM) is used to assess the macroeconomic consequences of extreme events. In the model, dynamic processes multiply the extreme event direct costs by a factor 20. Half of this increase comes from short-term processes, that long-term growth models cannot capture. The model exhibits also a bifurcation in GDP losses: for a given distribution of extremes, there is a value of the ability to fund reconstruction below which GDP losses increases dramatically. This bifurcation may partly explain why some poor countries that experience repeated natural disasters cannot develop. It also shows that changes in the distribution of extremes may entail significant GDP losses and that climate change may force a specific adaptation of the economic organization. These results show that averaging short-term processes like extreme events over the yearly time step of a long-term growth model can lead to inaccurately low assessments of the climate change damages.Dynamics; Extreme events; Economic impacts; Climate Change