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Almost sure exponential convergence to consensus of random gossip algorithms
Author(s) -
Picci Giorgio,
Taylor Thomas J.
Publication year - 2013
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2844
Subject(s) - ergodic theory , gossip , multiplicative function , convergence (economics) , exponential function , mathematics , selection (genetic algorithm) , class (philosophy) , discrete mathematics , computer science , algorithm , pure mathematics , mathematical analysis , artificial intelligence , economics , economic growth , psychology , social psychology
SUMMARY In this paper, we provide a proof of almost sure exponential convergence to consensus for a general class of ergodic edge selection processes. The proof is based on the multiplicative ergodic theorem of Oseledec and also applies to continuous time gossip algorithms. An example of exponential convergence in a non ergodic case is also discussed. Copyright © 2012 John Wiley & Sons, Ltd.