23 research outputs found
Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
The mathematical theory of gravitational lensing has revealed many generic
and global properties. Beginning with multiple imaging, we review
Morse-theoretic image counting formulas and lower bound results, and
complex-algebraic upper bounds in the case of single and multiple lens planes.
We discuss recent advances in the mathematics of stochastic lensing, discussing
a general formula for the global expected number of minimum lensed images as
well as asymptotic formulas for the probability densities of the microlensing
random time delay functions, random lensing maps, and random shear, and an
asymptotic expression for the global expected number of micro-minima. Multiple
imaging in optical geometry and a spacetime setting are treated. We review
global magnification relation results for model-dependent scenarios and cover
recent developments on universal local magnification relations for higher order
caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of
General Relativity and Gravitatio
Design of experiments for studying intergenotypic competition
International audienc
Conditions pour la convergence du nombre de franchissements vers le temps local. Application aux processus gaussiens et stables
National audienc
Conditions for convergence of number of crossings to the local time. Application to stable processes with independent increments and to gaussian processes
International audienc
Approximation des trajectoires et temps local des diffusions
National audienc
Construction du temps local a partir d'approximations de trajectoires. Prise en compte des relations de voisinage dans la planification et l'analyse d'experiences
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