Product of Random Stochastic Matrices and Distributed Averaging [electronic resource] / by Behrouz Touri.Material type: TextLanguage: English Series: Springer Theses, Recognizing Outstanding Ph.D. Research: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012Description: XIV, 142 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783642280030Subject(s): Engineering | Computer science | Distribution (Probability theory) | Mathematical statistics | Engineering | Control | Statistical Physics, Dynamical Systems and Complexity | Probability Theory and Stochastic Processes | Probability and Statistics in Computer Science | Statistical Theory and MethodsAdditional physical formats: Printed edition:: No titleDDC classification: 629.8 LOC classification: TJ212-225Online resources: Click here to access online
Introduction -- Products of Stochastic Matrices and Averaging Dynamics -- Ergodicity of Random Chains -- Infinite Flow Stability -- Implications -- Absolute Infinite Flow Property -- Averaging Dynamics in General State Spaces -- Conclusion and Suggestions for Future Works -- Appendices.
The thesis deals with averaging dynamics in a multiagent networked system, which is a main mechanism for diffusing the information over such networks. It arises in a wide range of applications in engineered physical networks (such as mobile communication and sensor networks), as well as social and economic networks. The thesis provides in depth study of stability and other phenomena characterizing the limiting behavior of both deterministic and random averaging dynamics. By developing new concepts, and using the tools from dynamic system theory and non-negative matrix theory, several novel fundamental results are rigorously developed. These contribute significantly to our understanding of averaging dynamics as well as to non-negative random matrix theory. The exposition, although highly rigorous and technical, is elegant and insightful, and accompanied with numerous illustrative examples, which makes this thesis work easily accessible to those just entering this field and will also be much appreciated by experts in the field.