10,957 research outputs found
Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials
This paper deals with the long time behaviour of solutions to the spatially
homogeneous Landau equation with hard potentials . We prove an exponential in
time convergence towards the equilibrium with the optimal rate given by the
spectral gap of the associated linearized operator. This result improves the
polynomial in time convergence obtained by Desvillettes and Villani
\cite{DesVi2}. Our approach is based on new decay estimates for the semigroup
generated by the linearized Landau operator in weighted (polynomial or
stretched exponential) -spaces, using a method develloped by Gualdani,
Mischler and Mouhot \cite{GMM}.Comment: 20 pages. Minor corrections, improvement on the presentatio
Quantitative and qualitative Kac's chaos on the Boltzmann's sphere
We investigate the construction of chaotic probability measures on the
Boltzmann's sphere, which is the state space of the stochastic process of a
many-particle system undergoing a dynamics preserving energy and momentum.
Firstly, based on a version of the local Central Limit Theorem (or Berry-Esseen
theorem), we construct a sequence of probabilities that is Kac chaotic and we
prove a quantitative rate of convergence. Then, we investigate a stronger
notion of chaos, namely entropic chaos introduced in \cite{CCLLV}, and we
prove, with quantitative rate, that this same sequence is also entropically
chaotic. Furthermore, we investigate more general class of probability measures
on the Boltzmann's sphere. Using the HWI inequality we prove that a Kac chaotic
probability with bounded Fisher's information is entropically chaotic and we
give a quantitative rate. We also link different notions of chaos, proving that
Fisher's information chaos, introduced in \cite{HaurayMischler}, is stronger
than entropic chaos, which is stronger than Kac's chaos. We give a possible
answer to \cite[Open Problem 11]{CCLLV} in the Boltzmann's sphere's framework.
Finally, applying our previous results to the recent results on propagation of
chaos for the Boltzmann equation \cite{MMchaos}, we prove a quantitative rate
for the propagation of entropic chaos for the Boltzmann equation with
Maxwellian molecules.Comment: 51 pages, to appear in Ann. Inst. H. Poincar\'e Probab. Sta
Sometimes the impact factor outshines the H index
Journal impact factor (which reflects a particular journal's quality) and H index (which reflects the number and quality of an author's publications) are two measures of research quality. It has been argued that the H index outperforms the impact factor for evaluation purposes. Using articles first-authored or last-authored by board members of Retrovirology, we show here that the reverse is true when the future success of an article is to be predicted. The H index proved unsuitable for this specific task because, surprisingly, an article's odds of becoming a 'hit' appear independent of the pre-eminence of its author. We discuss implications for the peer-review process
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