Geodesic
A characteristic polynomial for the transition probability matrix of correlated random walks on a graph
Takashi Komatsu1 ; Norio Konno2 ; Iwao Sato3
1The University of Tokyo
2Yokohama National University
3Oyama National College of Technology
The electronic journal of combinatorics, Tome 28 (2021) no. 4
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We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph $G$, and present a formula for the characteristic polynomial of the transition probability matrix of this CRW by using a determinant expression for the generalized weighted zeta function of $G$. As an application, we give the spectrum of the transition probability matrices for the CRWs induced from the Grover matrices of regular graphs and semiregular bipartite graphs. Furthermore, we consider another type of the CRW on a graph.
DOI : 10.37236/10108
Classification : 05C81, 05C50, 05C31, 15A15, 11M38, 11M41
Mots-clés : Grover matrix, Grover walk on a graph, correlated random walk

Takashi Komatsu   1   ; Norio Konno  2   ; Iwao Sato  3

1 The University of Tokyo
2 Yokohama National University
3 Oyama National College of Technology 
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     title = {A characteristic polynomial for the transition probability matrix of correlated random walks on a graph},
     journal = {The electronic journal of combinatorics},
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Takashi  Komatsu ; Norio Konno; Iwao Sato. A characteristic polynomial for the transition probability matrix of correlated random walks on a graph. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/10108

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