7 citations · 8 across the 3 of their papers we have counts for
7 papers
Regularity dimensions: quantifying doubling and uniform perfectness
Douglas C. Howroyd
We study the upper and lower regularity dimensions in relation to the notions of doubling and uniformly perfect. These two regularity properties are closely related which is quanti…
On the Hausdorff dimension of microsets
Jonathan M. Fraser, Douglas C. Howroyd, Antti Käenmäki +1
We investigate how the Hausdorff dimensions of microsets are related to the dimensions of the original set. It is known that the maximal dimension of a microset is the Assouad dime…
Dimension growth for iterated sumsets
Jonathan M. Fraser, Douglas C. Howroyd, Han Yu
We study dimensions of sumsets and iterated sumsets and provide natural conditions which guarantee that a set satisfies $\overline{\dim}_\text{B} F+F > \ov…
Assouad dimension of random processes
Douglas Howroyd, Han Yu
In this paper we study the Assouad dimension of graphs of certain Lévy processes and functions defined by stochastic integrals. We do this by introducing a convenient condition whi…
On the upper regularity dimensions of measures
Jonathan M. Fraser, Douglas C. Howroyd
We study the \emph{upper regularity dimension} which describes the extremal local scaling behaviour of a measure and effectively quantifies the notion of \emph{doubling}. We conduc…
Assouad type dimensions for certain sponges with a weak coordinate ordering condition
Douglas Howroyd
Recently self-affine sponges have been shown to be interesting counter-examples to several previously open problems. One class of recently studied sponges are Bedford-McMullen spon…