论文标题
抽象度量空间中的动态schrödinger问题
The dynamical Schrödinger problem in abstract metric spaces
论文作者
论文摘要
在本文中，我们在抽象度量空间上介绍了动力学的schrödinger问题，该问题定义为广泛的熵和Fisher信息功能。在非常温和的假设下，我们证明了噪声参数$ \ varepsilon \ downarrow 0 $的通用伽马连接结果。我们还研究了与驱动熵的测量凸的联系，并研究了熵成本对参数$ \ varepsilon $的依赖性。讨论了一些示例和应用。
In this paper we introduce the dynamical Schrödinger 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.
