P. Allaart

activity

20062023

most citedOn the continuity of the Hausdorff dimension of the univoque set

17 citations · 59 across the 22 of their papers we have counts for

collaborators

Showing 2018Show all

4 papers · 1 filter

math.DS2018

An algebraic approach to entropy plateaus in non-integer base expansions

Pieter C. Allaart

For a positive integer $M$ and a real base $q \in (1, M + 1]$ , let $U_{q}$ denote the set of numbers having a unique expansion in base $q$ over the alphabet ${0, 1, \dots, M}$ , 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 $n$ independent, identically distributed random variables are observed sequentially and the objective is t…

math.DS2018★ 9 cited

Relative bifurcation sets and the local dimension of univoque bases

Pieter Allaart, Derong Kong

Fix an alphabet $A = {0, 1, \dots, M}$ with $M \in N$ . The univoque set $U$ of bases $q \in (1, M + 1)$ in which the number $1$ has a unique expansion over the alphabet $A…

math.DS2018★ 17 cited

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 $U_{q}$ of numbers having a uniq…