2013 Fiscal Year Final Research Report
A study on relationships between stochastic and quantum models and random graph structures
| Project/Area Number |
23740093
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kanagawa University |
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Principal Investigator |
IDE Yusuke 神奈川大学, 工学部, 助教 (70553999)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 量子ウォーク / 固有空間解析 |
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| Research Abstract |
In this study, we concentrate on analysis of transition probabilities of discrete-time and continuous-time quantum walks on various graphs including random graphs. For the discrete-time case, we obtain some limit theorems for long-time average of the transition probabilities by detailed study of eigenspace of the Jacobi matrices. For the continuous-time case, we show relationships between local graph structures and the transition probabilities by detailed study of eigenspace of the Laplacian matrices.
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