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Your search keyword '"Shunya Tamura"' showing total 4 results
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4 results on '"Shunya Tamura"'

1. Return Probability of Quantum and Correlated Random Walks

Author

Chusei Kiumi, Norio Konno, and Shunya Tamura

Subjects
quantum walk, correlated random walk, return probability, elliptic integral, Legendre polynomial, Science, Astrophysics, QB460-466, Physics, QC1-999
Abstract

The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional integer lattice by the path counting method. We show that the return probability of both quantum and correlated random walks can be expressed in terms of the Legendre polynomial. Moreover, the generating function of the return probability can be written in terms of elliptic integrals of the first and second kinds for the quantum walk.

Published
2022
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3. On the average hitting times of the squares of cycles

Author

Yoshiaki Doi, Norio Konno, Tomoki Nakamigawa, Tadashi Sakuma, Etsuo Segawa, Hidehiro Shinohara, Shunya Tamura, Yuuho Tanaka, and Kosuke Toyota

Subjects
Applied Mathematics, FOS: Mathematics, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Combinatorics (math.CO)
Abstract

The exact formula for the average hitting time (HT, as an abbreviation) of simple random walks from one vertex to any other vertex on the square $C^2_N$ of an $N$-vertex cycle graph $C_N$ was given by N. Chair [\textit{Journal of Statistical Physics}, \textbf{154} (2014) 1177-1190]. In that paper, the author gives the expression for the even $N$ case and the expression for the odd $N$ case separately. In this paper, by using an elementary method different from Chair (2014), we give a much simpler single formula for the HT's of simple random walks on $C^2_N$. Our proof is considerably short and fully combinatorial, in particular, has no-need of any spectral graph theoretical arguments. Not only the formula itself but also intermediate results through the process of our proof describe clear relations between the HT's of simple random walks on $C^2_N$ and the Fibonacci numbers.

Published
2022

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