Approaching consensus can be delicate when positions harden

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

doi:10.1016/0304-4149(86)90008-6

Approaching consensus can be delicate when positions harden

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	315-322
Number of pages	8
Journal	Stochastic Processes and their Applications
Volume	22
Issue number	2
DOIs	https://doi.org/10.1016/0304-4149(86)90008-6
State	Published - Jul 1986

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Access to Document

10.1016/0304-4149(86)90008-6

Cite this

@article{8ae4e1e508ad490382855c2970e950b7,

title = "Approaching consensus can be delicate when positions harden",

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.",

keywords = "ergodicity, inhomogeneous products, products of random nonnegative matrices, strong limit laws, zero-one laws, zeta function",

author = "Cohen, {Joel E.} and John Hajnal and Newman, {Charles M.}",

note = "Funding Information: J.E.C. acknowledges fellowships from the John Simon Guggenheim Memorial Foundation, New York, the Center for Advanced Study in the Behavioral Sciences, Stanford, and the John D. and Catherine T. MacArthur Foundation, Chicago; National Science Foundation grants DEBgO-11026 and BSR84-07461; and grants to the Center for Advanced Study from the National Institute of Mental Health (5T32MH14581-06) and the Exxon Education Foundation. C.M.N. acknowledges N.S.F. grant MCS80-19384. We are grateful for the help of Robert Axelrod, Morris DeGroot, Mr. and Mrs. William T. Golden and referees.",

year = "1986",

month = jul,

doi = "10.1016/0304-4149(86)90008-6",

language = "English (US)",

volume = "22",

pages = "315--322",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - Approaching consensus can be delicate when positions harden

AU - Cohen, Joel E.

AU - Hajnal, John

AU - Newman, Charles M.

N1 - Funding Information: J.E.C. acknowledges fellowships from the John Simon Guggenheim Memorial Foundation, New York, the Center for Advanced Study in the Behavioral Sciences, Stanford, and the John D. and Catherine T. MacArthur Foundation, Chicago; National Science Foundation grants DEBgO-11026 and BSR84-07461; and grants to the Center for Advanced Study from the National Institute of Mental Health (5T32MH14581-06) and the Exxon Education Foundation. C.M.N. acknowledges N.S.F. grant MCS80-19384. We are grateful for the help of Robert Axelrod, Morris DeGroot, Mr. and Mrs. William T. Golden and referees.

PY - 1986/7

Y1 - 1986/7

N2 - 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.

AB - 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.

KW - ergodicity

KW - inhomogeneous products

KW - products of random nonnegative matrices

KW - strong limit laws

KW - zero-one laws

KW - zeta function

UR - http://www.scopus.com/inward/record.url?scp=0004382880&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0004382880&partnerID=8YFLogxK

U2 - 10.1016/0304-4149(86)90008-6

DO - 10.1016/0304-4149(86)90008-6

M3 - Article

AN - SCOPUS:0004382880

SN - 0304-4149

VL - 22

SP - 315

EP - 322

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

Approaching consensus can be delicate when positions harden

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this