Cut-off method for endogeny of recursive tree processes

2016/10/21 by Victor Kleptsyn, Kleptsyn, Victor, Michele Triestino +1
Computer Science · Mathematics · #60B10 #60E15. Secondary 81T20 #82B44 #90C27 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Primary 60E05 #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1610.06946

openalex publication_date 2016/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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