Poset limits and exchangeable random posets

TL;DR

This paper develops a theory of limits for finite posets, analogous to graph limits, involving representations by functions and connections to exchangeable random infinite posets.

Contribution

It introduces a novel framework for understanding limits of posets using function representations and exchangeability, extending the graph limit theory.

Findings

Established a representation of poset limits via functions on probability spaces

Connected poset limits to exchangeable random infinite posets

Provided foundational results for the theory of poset limits

Abstract

We develop a theory of limits of finite posets in close analogy to the recent theory of graph limits. In particular, we study representations of the limits by functions of two variables on a probability space, and connections to exchangeable random infinite posets.