Paper Info
Title
On Ergodicity, Infinite Flow and Consensus in Random Models
Abstract
We consider the ergodicity and consensus problem for a discrete-time linear dynamic model driven by random stochastic matrices, which is equivalent to studying these concepts for the product of such matrices. Our focus is on the model where the random matrices have independent but time-variant distribution. We introduce a new phenomenon, the infinite flow, and we study its fundamental properties and relations with the ergodicity and consensus. The central result is the infinite flow theorem establishing the equivalence between the infinite flow and the ergodicity for a class of independent random models, where the matrices in the model have a common steady state in expectation and a feedback property. For such models, this result demonstrates that the expected infinite flow is both necessary and sufficient for the ergodicity. The result is providing a deterministic characterization of the ergodicity, which can be used for studying the consensus and average consensus over random graphs.
Year
DOI
Venue
2011
10.1109/TAC.2010.2091174
IEEE Trans. Automat. Contr.
Keywords
Field
DocType
Stochastic processes,Steady-state,Convergence,Analytical models,Time measurement,Vectors
Flow network,Consensus,Applied mathematics,Discrete mathematics,Mathematical optimization,Ergodicity,Random graph,Matrix (mathematics),Stochastic process,Matrix multiplication,Mathematics,Random matrix
Journal
Volume
Issue
ISSN
56
7
0018-9286
Citations 
PageRank 
References 
16
0.77
26
Authors
2
Name
Order
Citations
PageRank
Behrouz Touri117621.12
Angelia Nedic22323148.65