Limit theorems and absorption problems for one-dimensional correlated random walks

TL;DR

This paper explores the mathematical properties of correlated random walks, highlighting their similarities to quantum walks, and uses a specialized method to analyze their limit behaviors and absorption characteristics.

Contribution

It introduces the PQRS method for analyzing correlated random walks, bridging classical and quantum walk theories with new analytical tools.

Findings

Established limit theorems for correlated random walks

Analyzed absorption probabilities using the PQRS method

Demonstrated structural similarities between classical and quantum walks

Abstract

There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between both walks and study limit theorems and absorption problems for correlated random walks by our PQRS method, which was used in our analysis of quantum walks.