3 papers
math.PR2017
Dependence between Path-length and Size in Random Digital Trees
Michael Fuchs, Hsien-Kuei Hwang
We study the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic f…
math.NT2015
On Kurzweil's 0-1 Law in Inhomogeneous Diophantine Approximation
Michael Fuchs, Dong Han Kim
We give a sufficient and necessary condition such that for almost all \[ \|nθ-s\|<ψ(n)\qquad\text{for infinitely many}\ n\in{\mathbb N}, \] where is fixed and…
math.CO2010
Asymptotic variance of random symmetric digital search trees
Hsien-Kuei Hwang, Michael Fuchs, Vytas Zacharovas
Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such…