@article{EJP871,
author = {Mikhail Lifshits and Werner Linde},
title = {Random Gaussian Sums on Trees},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {16},
year = {2011},
keywords = {Gaussian processes, processes indexed by trees, bounded processes, summation on trees, metric entropy},
abstract = {Let $T$ be a tree with induced partial order. We investigate a centered Gaussian process $X$ indexed by $T$ and generated by weight functions. In a first part we treat general trees and weights and derive necessary and sufficient conditions for the a.s. boundedness of $X$ in terms of compactness properties of $(T,d)$. Here $d$ is a special metric defined by the weights, which, in general, is not comparable with the Dudley metric generated by $X$. In a second part we investigate the boundedness of $X$ for the binary tree. Assuming some mild regularity assumptions about on weight, we completely characterize homogeneous weights with $X$ being a.s. bounded.},
pages = {no. 24, 739-763},
issn = {1083-6489},
doi = {10.1214/EJP.v16-871},
url = {http://ejp.ejpecp.org/article/view/871}}