# Normal Variance Mixture with Arcsine Law of an Interpolating Walk Between Persistent Random Walk and Quantum Walk

## TL;DR

This paper introduces a model that smoothly transitions between quantum and classical random walks, showing a unique statistical distribution.

## Contribution

A new model that interpolates between quantum and persistent random walks with a single parameter.

## Key findings

- The model's limit distribution follows a normal variance mixture with arcsine law.
- The interpolation reveals a continuous transition between quantum and classical walk behaviors.

## Abstract

We propose a model that interpolates between quantum walks and persistent (correlated) random walks using one parameter on the one-dimensional lattice. We show that the limit distribution is described by the normal variance mixture with the arcsine law.