On a $\psi_1$ - norm estimate of sum of dependent random variables using simple random walk on graph

TL;DR

This paper derives a $\, ext{ extbackslash psi}_1$-norm estimate for the sum of dependent Rademacher variables, utilizing a simple random walk on a graph to handle dependencies.

Contribution

It introduces a novel method to estimate the $\, ext{ extbackslash psi}_1$-norm of dependent variables using graph-based random walk techniques.

Findings

Established a $\, ext{ extbackslash psi}_1$-norm bound for dependent Rademacher sums

Applied graph-based random walk to dependency structures

Extended classical independent variable results to dependent cases

Abstract

We obtained a $\psi_1$ estimate for the sum of Rademacher random variables under condition that they are dependent.