Work

Return probabilities and orthogonal polynomials for RWs and QWs

Year: 2025

Type: conference-paper

Abstract: In this paper, we focus on discrete-time random walks (DTRWs) on the path graph with reflecting walls. Also we consider the corresponding continuous-time random walks (CTRWs), discrete-time quantum walks (DTQWs) and continuous-time quantum walks (CTQWs). We give formulas for the return probabilities of these four walks (DTRWs, CTRWs, DTQWs, CTQWs) at the boundary point of the path graph and discuss their relationships. Furthermore, by considering the Ehrenfest model, we derive the scaling limit theorems for the return probabilities of both the CTRW and the CTQW.

Source: Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications

DOI: 10.5687/sss.2025.17

Authors: Yusuke Ide, Norio Konno, Tomoyuki Terada

Institutions: Nihon University, Ritsumeikan University, Kanazawa Institute of Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7117236195

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Cites: 3

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