A survey of max-type recursive distributional equations

David J. Aldous; Antar Bandyopadhyay

doi:10.1214/105051605000000142

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A survey of max-type recursive distributional equations

David J. Aldous·Antar Bandyopadhyay

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Abstract

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 =^d g((ξ_i,X_i),i\geq 1). Here (ξ_i) and g(\cdot) are given and the X_i are independent copies of the unknown distribution X. We survey this area, emphasizing examples where the function g(\cdot) is essentially a ``maximum'' or ``minimum'' function. We draw attention to the theoretical question of endogeny: in the associated recursive tree process X_i, are the X_i measurable functions of the innovations process (ξ_i)?

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David J. Aldous, Antar Bandyopadhyay. 2005-05-20. A survey of max-type recursive distributional equations. https://doi.org/10.1214/105051605000000142

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