scholarly journals The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances

2017 ◽  
Vol 10 (4) ◽  
pp. 919-933 ◽  
Author(s):  
Jonathan Zinsl ◽  
Keyword(s):  
Fisher Information ◽  
Gradient Flow ◽  
Information Functional ◽  
Generalized Fisher Information ◽  
Wasserstein Distances

AN INEQUALITY BY GIANAZZA, SAVARÉ AND TOSCANI AND ITS APPLICATIONS TO THE VISCOUS QUANTUM EULER MODEL

2013 ◽  
Vol 15 (05) ◽  
pp. 1250067 ◽  
Author(s):  
XIANGSHENG XU
Keyword(s):  
Weak Solution ◽  
Diffusion Equation ◽  
Boundary Value Problem ◽  
Fisher Information ◽  
Gradient Flow ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Drift Diffusion ◽  
Euler Model ◽  
Initial Boundary Value

In this paper we present a simplified version of a coercivity inequality due to Gianazza, Savaré, and Toscani [The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation, Arch. Ration. Mech. Anal.194 (2009) 133–220]. Then we use the inequality to construct a weak solution to the initial-boundary value problem for the viscous quantum Euler model.

scholarly journals REMARKS ABOUT MIXED DISCRIMINANTS AND VOLUMES

2014 ◽  
Vol 16 (02) ◽  
pp. 1350031 ◽  
Author(s):  
S. ARTSTEIN-AVIDAN ◽  
D. FLORENTIN ◽  
Y. OSTROVER
Keyword(s):  
Fisher Information ◽  
Convex Sets ◽  
Compact Convex ◽  
Convex Bodies ◽  
Mixed Volumes ◽  
Information Functional ◽  
Geometric Analogue

In this note we prove certain inequalities for mixed discriminants of positive semi-definite matrices, and mixed volumes of compact convex sets in ℝn. Moreover, we discuss how the latter are related to the monotonicity of an information functional on the class of convex bodies, which is a geometric analogue of the classical Fisher information.

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