تقرير
The dynamical Schr\'odinger problem in abstract metric spaces
العنوان: | The dynamical Schr\'odinger problem in abstract metric spaces |
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المؤلفون: | Monsaingeon, Léonard, Tamanini, Luca, Vorotnikov, Dmitry |
سنة النشر: | 2020 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Mathematics - Metric Geometry, Mathematics - Optimization and Control, 49J45, 49Q20, 58B20 |
الوصف: | In this paper we introduce the dynamical Schr\"odinger problem on abstract metric spaces, defined for a wide class of entropy and Fisher information functionals. Under very mild assumptions we prove a generic Gamma-convergence result towards the geodesic problem as the noise parameter $\varepsilon\downarrow 0$. We also investigate the connection with geodesic convexity of the driving entropy, and study the dependence of the entropic cost on the parameter $\varepsilon$. Some examples and applications are discussed. Comment: Accepted in Advances in Mathematics |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2012.12005 |
رقم الأكسشن: | edsarx.2012.12005 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |