Moment duality and propagation of exchangeability

Adrián González Casanova; Ariel Offenstadt; Arno Siri-Jégousse

Moment duality and propagation of exchangeability

Probability 2026-06-26 v1

Authors: Adrián González Casanova , Ariel Offenstadt , Arno Siri-Jégousse

Abstract

We identify necessary and sufficient conditions for a class of random mappings to send exchangeable $\{0,1\}$ -sequences to other exchangeable $\{0,1\}$ -sequences. We call this property the propagation of exchangeability, and show that any mapping that propagates exchangeability induces a pair of forward- and backward-in-time processes that are moment duals. This establishes a transparent, tractable, and applicable connection between moment duality and the propagation of exchangeability. We illustrate the usefulness of our results by constructing lookdown models for $\Xi$ -Fleming--Viot processes with frequency-dependent selection.

Keywords

moment duality exchangeability random mappings lookdown model xi-fleming-viot process

Cite

@article{arxiv.2606.28174,
  title  = {Moment duality and propagation of exchangeability},
  author = {Adrián González Casanova and Ariel Offenstadt and Arno Siri-Jégousse},
  journal= {arXiv preprint arXiv:2606.28174},
  year   = {2026}
}