Multipopulation Spin Models: A View from Large Deviations Theoretic Window
Joint Authors
Osabutey, Godwin
Opoku, Alex Akwasi
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-11-01
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
This paper studies large deviations properties of vectors of empirical means and measures generated as follows.
Consider a sequence X1,X2,…,Xn of independent and identically distributed random variables partitioned into d-subgroups with sizes n1,…,nd.
Further, consider a d-dimensional vector mn whose coordinates are made up of the empirical means of the subgroups.
We prove the following.
(1) The sequence of vector of empirical means mn satisfies large deviations principle with rate n and rate function I, when the sequence X1,X2,…,Xn is Rl valued, with l≥1.
(2) Similar large deviations results hold for the corresponding sequence of vector of empirical measures Ln if Xi’s, i=1,2,…,n, take on finitely many values.
(3) The rate functions for the above large deviations principles are convex combinations of the corresponding rate functions arising from the large deviations principles of the coordinates of mn and Ln.
The probability distributions used in the convex combinations are given by α=(α1,…,αd)=limn→∞1/n(n1,…,nd).
These results are consequently used to derive variational formula for the thermodynamic limit for the pressure of multipopulation Curie-Weiss (I.
Gallo and P.
Contucci (2008), and I.
Gallo (2009)) and mean-field Pott’s models, via a version of Varadhan’s integral lemma for an equicontinuous family of functions.
These multipopulation models serve as a paradigm for decision-making context where social interaction and other socioeconomic attributes of individuals play a crucial role.
American Psychological Association (APA)
Opoku, Alex Akwasi& Osabutey, Godwin. 2018. Multipopulation Spin Models: A View from Large Deviations Theoretic Window. Journal of Mathematics،Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1193604
Modern Language Association (MLA)
Opoku, Alex Akwasi& Osabutey, Godwin. Multipopulation Spin Models: A View from Large Deviations Theoretic Window. Journal of Mathematics No. 2018 (2018), pp.1-13.
https://search.emarefa.net/detail/BIM-1193604
American Medical Association (AMA)
Opoku, Alex Akwasi& Osabutey, Godwin. Multipopulation Spin Models: A View from Large Deviations Theoretic Window. Journal of Mathematics. 2018. Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1193604
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193604