Ergodicity and totality of partitions associated with the RSK correspondence

TL;DR

This paper investigates the long-term behavior of partitions linked to the RSK correspondence in Bernoulli measure spaces, focusing on their ergodic and total properties.

Contribution

It provides new insights into the asymptotic properties of partitions related to RSK in probabilistic measure spaces, expanding understanding of their ergodic behavior.

Findings

Characterization of ergodicity in partitions

Identification of totality conditions for partitions

Asymptotic analysis of partition sequences

Abstract

We study asymptotic properties of sequences of partitions ($\sigma$\nobreakdash-algebras) in spaces with Bernoulli measures associated with the Robinson--Schensted--Knuth correspondence.