6,308 research outputs found
Asympotic behavior of the total length of external branches for Beta-coalescents
We consider a -coalescent and we study the asymptotic behavior of
the total length of the external branches of the associated
-coalescent. For Kingman coalescent, i.e. , the result
is well known and is useful, together with the total length , for Fu
and Li's test of neutrality of mutations% under the infinite sites model
asumption . For a large family of measures , including
Beta with , M{\"o}hle has proved asymptotics
of . Here we consider the case when the measure is
Beta, with . We prove that
converges in to
. As a consequence, we get that
converges in probability to . To prove the
asymptotics of , we use a recursive construction of the
-coalescent by adding individuals one by one. Asymptotics of the
distribution of 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
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
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