تقرير
The dynamical Schr\'odinger problem in abstract metric spaces
| العنوان: | The dynamical Schr\'odinger problem in abstract metric spaces |
|---|---|
| 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. |