By Dominique Bakry,Ivan Gentil,Michel Ledoux
The current quantity is an in depth monograph at the analytic and geometric elements of Markov diffusion operators. It makes a speciality of the geometric curvature houses of the underlying constitution with a purpose to learn convergence to equilibrium, spectral bounds, practical inequalities resembling Poincaré, Sobolev or logarithmic Sobolev inequalities, and numerous bounds on suggestions of evolution equations. whilst, it covers a wide category of evolution and partial differential equations.
The ebook is meant to function an advent to the topic and to be available for starting and complex scientists and non-specialists. concurrently, it covers quite a lot of effects and strategies from the early advancements within the mid-eighties to the newest achievements. As such, scholars and researchers drawn to the fashionable elements of Markov diffusion operators and semigroups and their connections to analytic sensible inequalities, probabilistic convergence to equilibrium and geometric curvature will locate it specifically precious. chosen chapters is additionally used for complex classes at the topic.
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Analysis and Geometry of Markov Diffusion Operators (Grundlehren der mathematischen Wissenschaften) by Dominique Bakry,Ivan Gentil,Michel Ledoux