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Wolfowitz's theorem and consensus algorithms in Hadamard spaces


Author: P. Grohs
Journal: Proc. Amer. Math. Soc. 143 (2015), 4403-4414
MSC (2010): Primary 53C23, 60J20, 65P99
DOI: https://doi.org/10.1090/proc/12513
Published electronically: June 16, 2015
MathSciNet review: 3373939
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Abstract: We provide a generalization of Wolfowitz's theorem on the products of stochastic, indecomposable and aperiodic (SIA) matrices to metric spaces with nonpositive curvature. As a result we show convergence for a wide class of distributed consensus algorithms operating on these spaces.


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Additional Information

P. Grohs
Affiliation: Swiss Federal Institute of Technology - Zurich, Department of Mathematics, Raem- istrasse 101, 8092 Zurich, Switzerland

DOI: https://doi.org/10.1090/proc/12513
Keywords: SIA matrices, consensus algorithms, Hadamard space, Wolfowitz theorem
Received by editor(s): August 25, 2012
Received by editor(s) in revised form: March 20, 2014
Published electronically: June 16, 2015
Additional Notes: The research of the author was partly supported by the European Research Council under grant ERC AdG 247277, as well as by the Swiss National Fund under grant SNF 200021_140635
Communicated by: Walter Van Assche
Article copyright: © Copyright 2015 American Mathematical Society