An infinite stochastic model of social network formation

Thomas M. Liggett; Silke W.W. Rolles

doi:10.1016/j.spa.2004.03.011

An infinite stochastic model of social network formation

Thomas M. Liggett, Silke W.W. Rolles

University of California at Los Angeles

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

10 Scopus citations

Abstract

We consider an infinite interacting particle system in which individuals choose neighbors according to evolving sets of probabilities. If x chooses y at some time, the effect is to increase the probability that y chooses x at later times. We characterize the extremal invariant measures for this process. In an extremal equilibrium, the set of individuals is partitioned into finite sets called stars, each of which includes a "center" that is always chosen by the other individuals in that set.

Original language	English
Pages (from-to)	65-80
Number of pages	16
Journal	Stochastic Processes and their Applications
Volume	113
Issue number	1
DOIs	https://doi.org/10.1016/j.spa.2004.03.011
State	Published - Sep 2004
Externally published	Yes

Keywords

Interacting particle system
Invariant measures
Network formation

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10.1016/j.spa.2004.03.011

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AB - We consider an infinite interacting particle system in which individuals choose neighbors according to evolving sets of probabilities. If x chooses y at some time, the effect is to increase the probability that y chooses x at later times. We characterize the extremal invariant measures for this process. In an extremal equilibrium, the set of individuals is partitioned into finite sets called stars, each of which includes a "center" that is always chosen by the other individuals in that set.

KW - Interacting particle system

KW - Invariant measures

KW - Network formation

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ER -

An infinite stochastic model of social network formation

Abstract

Keywords

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