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Probability and Combinatorics

Tuesday, April 2, 2024 - 3:30pm

Paul Jung

Fordham University


Temple University

Wachman 617

We discuss a class of partially exchangeable random arrays which generalizes the notion of hierarchical exchangeability introduced in Austin and Panchenko (2014). We say that our partially exchangeable arrays are DAG-exchangeable since their partially exchangeable structure is governed by a collection of Directed Acyclic Graphs (DAG). More specifically, such a random array is indexed by N^|V| for some DAG, G = (V,E), and its exchangeability structure is governed by the edge set E. We prove a representation theorem which generalizes the Aldous-Hoover and Austin-Panchenko representation theorems.