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On taking up position in a group: A continuous‐time Markov model for biased random movement
Author(s) -
Grimmett Geoffrey,
Treisman Michel
Publication year - 1980
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1980.tb00611.x
Subject(s) - asymptote , group (periodic table) , movement (music) , position (finance) , jump , mathematics , markov process , markov chain , space (punctuation) , preference , statistical physics , degree (music) , statistics , mathematical analysis , computer science , physics , finance , quantum mechanics , acoustics , economics , operating system
A model is developed for movement by members of a group when this movement is random but is affected by a preference for a particular region of the space occupied by the group. Asymptotic distributions are derived from a continuous‐time Markovian model for the case in which a group member may move to any unoccupied location in one jump, and a method for estimating the degree of attraction of the preferred region is given. Such a group is described as ‘fluid’. A viscous' group is defined as one in which interchanges take place one step at a time. Movement in such groups was simulated on a computer and some results are given, including the apparently paradoxical finding that an approach tendency will be more strongly evident at asymptote if access to the preferred region is difficult than if it is easy.