4 papers
math.CA2019
The pointwise Hölder spectrum of general self-affine functions on an interval
Pieter Allaart
This paper gives the pointwise Hölder (or multifractal) spectrum of continuous functions on the interval whose graph is the attractor of an iterated function system consist…
math.DS2018
An algebraic approach to entropy plateaus in non-integer base expansions
Pieter C. Allaart
For a positive integer and a real base , let denote the set of numbers having a unique expansion in base over the alphabet , a…
math.PR2018
A random walk version of Robbins' problem: small horizon
Pieter C. Allaart, Andrew Allen
In Robbins' problem of minimizing the expected rank, a finite sequence of independent, identically distributed random variables are observed sequentially and the objective is t…
math.DS2018
On the continuity of the Hausdorff dimension of the univoque set
Pieter Allaart, Derong Kong
In a recent paper [Adv. Math. 305:165--196, 2017], Komornik et al.~proved a long-conjectured formula for the Hausdorff dimension of the set of numbers having a uniq…