Reference : Gaussian approximation in random minimal directed spanning trees
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/47064
 Title : Gaussian approximation in random minimal directed spanning trees Language : English Author, co-author : Bhattacharjee, Chinmoy [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >] Publication date : 2021 Journal title : Random Structures and Algorithms Publisher : John Wiley & Sons Pages : 1-31 Peer reviewed : Yes (verified by ORBilu) ISSN : 1042-9832 City : Hoboken Country : NJ Abstract : [en] We study the total $\alpha$-powered length of the rooted edges in a random minimal directed spanning tree - first introduced in \cite{BR04} - on a Poisson process with intensity $s \ge 1$ on the unit cube $[0,1]^d$ for $d \ge 3$. While a Dickman limit was proved in \cite{PW04} in the case of $d=2$, in dimensions three and higher, \cite{BLP06} showed a Gaussian central limit theorem when $\alpha=1$, with a rate of convergence of the order $(\log s)^{-(d-2)/4} (\log \log s)^{(d+1)/2}$. In this paper, we extend these results and prove a central limit theorem in any dimension $d \ge 3$ for any $\alpha>0$. Moreover, making use of recent results in Stein's method for region-stabilizing functionals, we provide presumably optimal non-asymptotic bounds of the order $(\log s)^{-(d-2)/2}$ on the Wasserstein and the Kolmogorov distances between the distribution of the total $\alpha$-powered length of rooted edges, suitably normalized, and that of a standard Gaussian random variable. Permalink : http://hdl.handle.net/10993/47064

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
MDST_RSA.pdfAuthor postprint419.94 kBView/Open

All documents in ORBilu are protected by a user license.