Walk/Zeta Correspondence

Abstract

Our previous work presented explicit formulas for the generalized zeta function and the generalized Ihara zeta function corresponding to the Grover walk and the positive-support version of the Grover walk on the regular graph via the Konno-Sato theorem, respectively. This paper extends these walks to a class of walks including random walks, correlated random walks, quantum walks, and open quantum random walks on the torus by the Fourier analysis.

31 pages

References in corpus (3)

• A note on the Grover walk and the generalized Ihara zeta function of the one-dimensional integer lattice
• Grover/Zeta Correspondence based on the Konno-Sato theorem
• A Characteristic Polynomial for The Transition Probability Matrix of A Correlated Random Walk on A Graph

Cited by in corpus (2)

• Walk/Zeta Correspondence for quantum and correlated random walks
• CTM/Zeta Correspondence