Almost sure convergence of random gossip algorithms

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2007, Pages 282-287

  Picci, Giorgio ^a   Taylor, Thomas ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

RANDOM PROCESSES; THEOREM PROVING;

RANDOM GOSSIP ALGORITHMS;

ALGORITHMS;

EID: 62749144127     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2007.4434573     Document Type: Conference Paper

References (15)

1. Ludwig Arnold, Random Dynamical Systems, Springer- Verlag, 1998.
2. A.Bensoussan and J. L. Menaldi, Difference Equations on Weighted Graphs, Journal of Convex Analysis, 12, 13-44, (2005).
3. B. Bollobas Modern Graph Theory, Springer graduate texts in mathematics, 1998.
4. S. Boyd, A. Ghosh, B. Prabhakar, D. Shah, Randomized Gossip Algorithms, IEEE Trans. Inf. Theor. 52, 2508-2530, (2006).
5. R. Cogburn,On Direct Convergence and Periodicity for Transition Probabilities of Markov Chains in Random Environments, Ann. Prob. 18, pp. 642-654(1990)
6. I.P. Cornfeld, S.V. Fomin and Y. Sinai, Ergodic Theory, Springer, 1982.
7. L.Elsner, I.Koltracht and M.Neumann, On the Convergence of Asynchronous Paracontractions with Application to Tomographic Rescon-struction from Incomplete Data, Linear Algebra and its Applications, 130, 65-82 (1990).
8. G. Golub and C. Van Loan, Matrix Computations, Johns Hopkins Studies in Math Sciences, 1996.
9. D. Kempe and J. Kleinberg and A. Demers, Spatial gossip and resource allocation protocols, Journal of the ACM, 51, 943-967, (2004).
10. S. Nelson and M. Neumann, Generalizations of the Projection Method with Applications to SOR Theory for Hermitian Positive Semidefinite Linear Systems, Numerische Mathematik 51, 123-141 (1987).
11. R. Olfati-Saber and R. Murray, Consensus problems in Networks of agents with swithching topoology and time delays, IEEE Transd Aut. Control, 49, 1520-1533, (2004).
12. V. I. Oseledec, A multiplicative ergodic theorem, Ljapunov characteristic numbers for dynamical systems, Trudy Moskov, Mat. Obsc, 19 (1968)
13. S. Orey: Markov Chains with Stochastically Stationary Transition Probabilities, Ann. Prob. 19, 907-928 (1991)
14. David Ruelle, Ergodic Theory on Differentiable Dynamical Systems, IHES Publications Mathématiques, 50:275-320 (1979).
15. P. Walters, An introduction to ergodic theory Springer Graduate Texts in Math. 1982.