4 papers
Mean dimension and rate-distortion function revisited
Rui Yang
Around the mean dimensions and rate-distortion functions, using some tools from local entropy theory this paper establishes the following main results: We prove that for non-…
Metric mean dimension and the variational principle for actions of amenable groups
Rui Yang, Xiaoyao Zhou
Metric mean dimension is a dynamical counterpart of the box dimension in fractal geometry to characterize the topological complexity of infinite entropy systems. The classical vari…
On the metric mean dimensions of saturated sets
Yong Ji, Junye Li, Rui Yang
From a geometric perspective, we employ metric mean dimension to investigate the set of generic points of invariant measures and saturated sets in infinite entropy systems. For sys…
Hessian matrix estimates of heat-type equations via Bismut-Stroock Hessian formula
Li-Juan Cheng, Rui-Yu Yang
In this paper, we establish a new global Hessian matrix estimate for heat-type equations on Riemannian manifolds using a Bismut-type Hessian formula. Our results feature fully expl…