# Characters and invariant random subgroups of the finitary symmetric group

## TL;DR

This paper explores the connection between indecomposable characters and ergodic invariant random subgroups of the finitary symmetric group, providing new interpretations and asymptotic analyses of Thoma characters.

## Contribution

It establishes a relationship between characters and invariant random subgroups, and interprets Thoma characters as limits of induced characters from Young subgroups.

## Key findings

- Character and subgroup relationship clarified
- Thoma characters as asymptotic limits demonstrated
- New perspective on finitary symmetric group characters

## Abstract

We will describe the relationship between the indecomposable characters of the finitary symmetric group and its ergodic invariant random subgroups; and we will interpret each Thoma character as an asymptotic limit of a naturally associated sequence of characters induced from linear characters of Young subgroups of finite symmetric groups.