A q-analogue of de Finetti's theorem

TL;DR

This paper develops a q-analogue of de Finetti's theorem using boundary problems for the q-Pascal graph, providing a characterization of invariant random spaces over finite fields under group actions.

Contribution

It introduces a novel q-analogue of de Finetti's theorem linked to boundary problems for the q-Pascal graph, extending classical results to finite fields.

Findings

Established a q-analogue of de Finetti's theorem.

Characterized invariant random spaces over F_q.

Connected the theorem to boundary problems in graph theory.

Abstract

A q-analogue of de Finetti's theorem is obtained in terms of a boundary problem for the q-Pascal graph. For q a power of prime this leads to a characterisation of random spaces over the Galois field F_q that are invariant under the natural action of the infinite group of invertible matrices with coefficients from F_q.