In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form $X\mathop{=}\limits^{d}\,g((\xi_{i},X_{i}),i\geq 1)$ . Here (ξi) and g(⋅) are given and the Xi are independent copies of the unknown distribution X. We survey this area, emphasizing examples where the function g(⋅) is essentially a “maximum” or “minimum” function. We draw attention to the theoretical question of endogeny: in the associated recursive tree process Xi, are the Xi measurable functions of the innovations process (ξi)?
Publié le : 2005-05-14
Classification:
Branching process,
branching random walk,
cavity method,
coupling from the past,
fixed point equation,
frozen percolation,
mean-field model of distance,
metric contraction,
probabilistic analysis of algorithms,
probability distribution,
probability on trees,
random matching,
60E05,
62E10,
68Q25,
82B44
@article{1115137969,
author = {Aldous, David J. and Bandyopadhyay, Antar},
title = {A survey of max-type recursive distributional equations},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 1047-1110},
language = {en},
url = {http://dml.mathdoc.fr/item/1115137969}
}
Aldous, David J.; Bandyopadhyay, Antar. A survey of max-type recursive distributional equations. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 1047-1110. http://gdmltest.u-ga.fr/item/1115137969/