A study on relationships between stochastic and quantum models and random graph structures
Project/Area Number |
23740093
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
Research Institution | Kanagawa University |
Principal Investigator |
IDE Yusuke 神奈川大学, 工学部, 助教 (70553999)
|
Project Period (FY) |
2011 – 2013
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | 量子ウォーク / 固有空間解析 / graph Laplacian / 直交多項式 / 有限グラフ / パス / 複雑ネットワーク / センサネットワーク |
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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Report
(4 results)
Research Products
(22 results)