# Hypergroups derived from random walks on some infinite graphs

## TL;DR

This paper extends Wildberger's method for constructing finite hermitian discrete hypergroups from random walks on certain graphs to infinite graphs, exploring conditions under which such hypergroups can be derived from infinite structures.

## Contribution

It demonstrates that Wildberger's hypergroup construction applies to specific infinite graphs and identifies conditions for hypergroup formation from infinite graph random walks.

## Key findings

- Hypergroups can be derived from random walks on certain infinite graphs.
- Conditions for hypergroup formation depend on graph structure.
- Extension of finite hypergroup construction to infinite graphs.

## Abstract

Wildberger gave a method to construct a finite hermitian discrete hypergroup from a random walk on a certain kind of graphs. In this article, we reveal that his method is applicable to a random walk on a certain kind of infinite graphs. Moreover, we make some observations of finite or infinite graphs on which a random walk produces a hermitian discrete hypergroup.