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Pré-Publication, Document De Travail Année : 2016

Cut-off method for endogeny of recursive tree processes

Résumé

Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process. We propose a new method of proving endogeny, which applies to various processes. As explicit examples, we establish endogeny of the random metrics on non-pivotal hierarchical graphs defined by multiplicative cascades and of mean-field optimization problems as the mean-field matching and travelling salesman problems in pseudo-dimension q>1.

Dates et versions

hal-01389493 , version 1 (28-10-2016)

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Victor A. Kleptsyn, Michele Triestino. Cut-off method for endogeny of recursive tree processes. 2016. ⟨hal-01389493⟩
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