Distance k-graphs of hypercube and q-Hermite polynomials

TL;DR

This paper demonstrates that certain weighted graphs derived from hypercube distance k-graphs can approximate q-Hermite polynomials of q-Gaussian variables using a specific matrix model.

Contribution

It introduces a novel matrix model that connects hypercube distance graphs with q-Hermite polynomials, advancing understanding of their relationship.

Findings

Weighted graphs on hypercube distance k-graphs approximate q-Hermite polynomials.

Provides an explicit matrix model for the approximation.

Establishes a new link between graph theory and q-Gaussian analysis.

Abstract

We will prove that some weighted graphs on the distance $k$-graph of hypercubes approximate the $q$-Hermite polynomial of a $q$-gaussian variable by providing an appropriate matrix model.