Approaching consensus can be delicate when positions harden

Joel E. Cohen, John Hajnal, Charles M. Newman

Research output: Contribution to journalArticle

Abstract

A model of consensus leads to examples in which the ergodic behavior of a nonstationary product of random nonnegative matrices depends discontinuously on a continuous parameter. In these examples, a product of random matrices, each of which is a scrambling stochastic matrix, changes from being weakly ergodic (asymptotically of rank 1) with probability 1 to being weakly ergodic with probability 0 as a parameter of the process changes smoothly.

Original languageEnglish (US)
Pages (from-to)315-322
Number of pages8
JournalStochastic Processes and their Applications
Volume22
Issue number2
DOIs
StatePublished - 1986

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Products of Random Matrices
Stochastic Matrix
Nonnegative Matrices
Random Matrices
Model
Process change

Keywords

  • ergodicity
  • inhomogeneous products
  • products of random nonnegative matrices
  • strong limit laws
  • zero-one laws
  • zeta function

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Mathematics(all)
  • Modeling and Simulation
  • Statistics and Probability

Cite this

Approaching consensus can be delicate when positions harden. / Cohen, Joel E.; Hajnal, John; Newman, Charles M.

In: Stochastic Processes and their Applications, Vol. 22, No. 2, 1986, p. 315-322.

Research output: Contribution to journalArticle

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