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Updated: Sep 13, 2025
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Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion
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Normal Variance Mixture with Arcsine Law of an Interpolating Walk Between Persistent Random Walk and Quantum Walk.
Saori Yoshino1, Honoka Shiratori2, Tomoki Yamagami2
1Graduate School of Environment and Information Sciences, Yokohama National University, Hodogaya, Yokohama 240-8501, Japan.
Entropy (Basel, Switzerland)
|July 29, 2025
Summary
We introduce a model that unifies quantum walks and persistent random walks on a 1D lattice. The study reveals that the limit distribution follows the arcsine law, a key finding in random walk analysis.
Area of Science:
- Probability theory
- Quantum mechanics
- Statistical physics
Background:
- Quantum walks and persistent random walks are distinct models of particle movement.
- Understanding their relationship can reveal new insights into stochastic processes.
Purpose of the Study:
- To develop a unified model interpolating between quantum walks and persistent random walks.
- To analyze the limit distribution of this novel model.
Main Methods:
- Development of a one-parameter model on a one-dimensional lattice.
- Mathematical analysis of the model's behavior in the limit.
Main Results:
- The proposed model successfully interpolates between quantum and persistent random walks.
- The limit distribution is characterized as a normal variance mixture with the arcsine law.
Conclusions:
- The unified model provides a bridge between quantum and classical random walk paradigms.
- The arcsine law emerges as a fundamental characteristic of this interpolated process.
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