# A common limit in large rank for Markov chains defined from representations of classical Lie algebras

## TL;DR

This paper demonstrates that Markov chains derived from classical Lie algebra representations have a universal limiting transition kernel as the rank increases, independent of the algebra type.

## Contribution

It establishes the existence of a universal limit for the transition kernels of these Markov chains across all classical Lie algebra types.

## Key findings

- Transition kernels converge as rank tends to infinity
- Limit kernel is independent of Lie algebra type
- Universal behavior observed in large-rank limit

## Abstract

From the datum of an integer partition and a classical Lie algebra, one can define a Markov chain on an associated multiplicative graph. For each classical family A, C, B, D, we thus obtain a sequence of Markov chain which is indexed by the rank of the considered algebra. In this article we show that, for each type, the transition kernel of the Markov chain has a limit when the rank tends to infinity. Moreover, the limit kernel does not depend on the considered type.