# Iterated partial summations applied to finite-support discrete distributions

## TL;DR

This paper explores iterated partial summations for discrete distributions with finite support, using the power method to establish the existence of limit distributions expressed via linear systems, supported by illustrative examples.

## Contribution

It introduces a novel application of the power method to analyze limit distributions of iterated partial summations for finite-support discrete distributions.

## Key findings

- Power method effectively proves existence of limit distributions.
- Limit distributions can be characterized as solutions to linear systems.
- Examples demonstrate the practical application of the approach.

## Abstract

The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases an effective tool to prove the existence of the limit distribution, which is then expressed as a solution of a system of linear equations. Some examples are presented.