Wanchun Shen

collaborators

3 papers

math.MG2019

Quasi-Assouad dimensions for random measures supported on $[0, 1]^{d}$

Wanchun Shen

We introduce a probability distribution on $P ([0, 1]^{d})$ , the space of all Borel probability measures on $[0, 1]^{d}$ . Under this distribution, almost all measures are shown…

math.CA2019

The $L^{q}$ -spectrum for a class of self-similar measures with overlap

Kathryn E. Hare, Kevin G. Hare, Wanchun Shen

It is known that the heuristic principle, referred to as the multifractal formalism, need not hold for self-similar measures with overlap, such as the $3$ -fold convolution of the C…

math.MG2018

The Entropy of Cantor--like measures

Kathryn E. Hare, Kevin G. Hare, Brian P. M. Morris +1

By a Cantor-like measure we mean the unique self-similar probability measure $μ$ satisfying $μ = \sum_{i = 0}^{m - 1} p_{i} μ \circ S_{i}^{- 1}$ where $% S_{i}(x)=\frac{x}{d}+\frac{i}{d}\cdo…

Quasi-Assouad dimensions for random measures supported on [0,1]d

The Lq-spectrum for a class of self-similar measures with overlap

The Entropy of Cantor--like measures

Quasi-Assouad dimensions for random measures supported on $[0, 1]^{d}$

The $L^{q}$ -spectrum for a class of self-similar measures with overlap