A widely studied model for generating sequences is to “evolve” them on a tree according to a symmetric Markov process. We prove that model trees tend to be maximally “far apart” in terms of variational distance.
@article{1159804991,
author = {Steel, M. A. and Sz\'ekely, L. A.},
title = {On the variational distance of two trees},
journal = {Ann. Appl. Probab.},
volume = {16},
number = {1},
year = {2006},
pages = { 1563-1575},
language = {en},
url = {http://dml.mathdoc.fr/item/1159804991}
}
Steel, M. A.; Székely, L. A. On the variational distance of two trees. Ann. Appl. Probab., Tome 16 (2006) no. 1, pp. 1563-1575. http://gdmltest.u-ga.fr/item/1159804991/