6533b7d9fe1ef96bd126ce69

RESEARCH PRODUCT

Cut-off method for endogeny of recursive tree processes

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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.