Variational relations for metric mean dimension and rate distortion dimension
Tao Wang
Abstract
<p style='text-indent:20px;'>Recently, Lindenstrauss and Tsukamoto established a double variational principle between mean dimension theory and rate distortion theory. The main purpose of this paper is to develop some new variational relations for the metric mean dimension and the rate distortion dimension. Inspired by the dimension theory of topological entropy, we introduce and explore the Bowen metric mean dimension of subsets. Besides, we give some new characterizations for the rate distortion dimension. Finally, the relation between the Bowen metric mean dimension of the set of generic points and the rate distortion dimension is also investigated.
Topics & Concepts
MathematicsDimension functionDimension (graph theory)Distortion (music)Metric (unit)Packing dimensionInductive dimensionIntrinsic dimensionEffective dimensionEntropy (arrow of time)Mathematical analysisHausdorff dimensionMinkowski–Bouligand dimensionTopology (electrical circuits)Pure mathematicsCombinatoricsStatisticsPhysicsQuantum mechanicsFractal dimensionFractalEconomicsCurse of dimensionalityAmplifierCMOSOptoelectronicsOperations managementMathematical Dynamics and FractalsAxon Guidance and Neuronal SignalingDigital Image Processing Techniques