A Conditional Curie–Weiss Model for Stylized Multi-group Binary Choice with Social Interaction

Opoku, Alex Akwasi; Edusei, Kwame Owusu; Ansah, Richard Kwame

doi:10.1007/s10955-018-1988-y

Cited by 14 publications

(13 citation statements)

References 19 publications

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“…Later, they were rediscovered as interesting models for statistical mechanics systems, see [18], [15], [8], [26], [24], as well as models for social interactions between several groups, e.g. in [17], [1], [28]. This latter approach follows very much the social re-interpretation for one group of the Curie-Weiss model in [6] or of the Hopfield model in [9] or [25].…”

Section: Introductionmentioning

confidence: 99%

Fluctuation Results for General Block Spin Ising Models

et al. 2020

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We study a block spin mean-field Ising model. For the vector of block magnetizations we prove Large Deviation Principles and Central Limit Theorems under general assumptions for the block interaction matrix. Using the exchangeable pair approach of Stein's method we are also able to establish a speed of convergence for the Central Limit Theorem for the vector of block magnetizations in the high temperature regime.

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Section: Introductionmentioning

confidence: 99%

Fluctuation Results for General Block Spin Ising Models

et al. 2020

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“…We propose, in this section, a discrete choice with social interaction model for energy conservation behaviour. The discussion here follows closely the presentations in [20,21]. Imagine there are N-energy users who are to decide on whether to conserve or not to conserve energy at some common time.…”

Section: Discrete Choice With Socialmentioning

confidence: 95%

A Statistical Mechanics Approach to the Study of Energy Use Behaviour

Osabutey

Opoku

Gyamfi

2020

Journal of Applied Mathematics

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This paper proposes a statistical mechanical model for the energy conservation behaviour of energy users. The model was inspired by the multipopulation Curie-Weiss model and the discrete choice with social interaction model. We demonstrate that the model integrates the sociopsychological, the economic, and the energy technologist viewpoints to energy management, allowing us to subject these perspectives to an empirical study.

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“…The detail analysis for continuous spin models and their phase diagram will be carried out in a future paper. We present the results for the Curie-Weiss and Potts's models here because we have already studied the thermodynamic limits of these models in [17,18].…”

Section: Applicationsmentioning

confidence: 99%

“…The large behaviour of the model is governed by the pressure function. It is known from [18] that the thermodynamic limit…”

Section: Multipopulation Curie-weiss Modelmentioning

confidence: 99%

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Multipopulation Spin Models: A View from Large Deviations Theoretic Window

Opoku

Osabutey

2018

Journal of Mathematics

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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.

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A Conditional Curie–Weiss Model for Stylized Multi-group Binary Choice with Social Interaction

Cited by 14 publications

References 19 publications

Fluctuation Results for General Block Spin Ising Models

Fluctuation Results for General Block Spin Ising Models

A Statistical Mechanics Approach to the Study of Energy Use Behaviour

Multipopulation Spin Models: A View from Large Deviations Theoretic Window

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