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INdAM Fellowship Programs in Mathematics and/or Applications cofunded by Marie Skłodowska-Curie Actions



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Micaela Fedele

INdAM-COFUND Outgoing fellow between 2012-07-05 and 2014-07-04

Project information

Title

INSYDER: Interacting particles systems and applications to the description of socioeconomical phenomena

Outgoing host organisation                                       Return host organisation

New York University                                                               Università  degli Studi di Bologna

Broadway 726, 2nd floor                                                       Dipartimento di Matematica

10003 1526 New York                                                            Piazza di Porta San Donato, 5
United States of America                                                       40126 Bologna, Italy

http://www.nyu.edu/                                                            http://www.unibo.it/

 

Abstract

The project focuses on the study of several statistical mechanics models that may be used in the attempt to understand and forecast collective human behavior concerning socio-economical matters. The analysis of these models from both theoretical and applicative point of view addresses an increasing demand of studying socio-economical phenomena on solid mathematical grounds.

In particular the project will develop such a dual analysis for a generalization of the Curie-Weiss model in which particles are partitioned into an arbitrary number of groups and both the interaction and the noninteraction parameters take different values depending on the groups particles belong to. This also corresponds to a generalization of the Discrete Choice theory developed by Mc Fadden in which peer to peer effects were not taken into account.

On the mathematical level the project plans to describe the equilibrium limiting distribution of the random vector whose components are the sums of spins of each group by extending methods and techniques used by Ellis, Newman and Rosen to study the same problem for the Curie-Weiss model. The relevance of such study is that the critical phase of the model, which the featured applications crucially depend upon, is structurally related to the probability distributions of that random vector. A second important step of the project will be fitting the model against empirical data in order to enable quantitative predictions.

Subsequent investigations will apply the same approach to more refined cases such as the
herrington-Kirkpatrick and models on random graph.

Fellow information

Research interests

Statistical Mechanics, Probability
Theory. Main topics include: Interacting particle systems; extentions
of the central limit theorem; inverse problem for mean field models;
application of interacting models to social and economical
sciences.

Previous positions, awards

  • 2010-2012: Postdoctoral fellow, Dipartimento di Matematica, Università degli Studi di Bologna
    Research project: Statistical mechanics models for the study of interactinmg populations. Supervisor: P. Contucci.

Publications, preprints, other works

  1. M. Fedele, P. Contucci, Scaling Limits for Multispecies Statistical Mechanics Mean-Field Models, Journal of Statistical Physics, vol. 144, N. 6, pp. 1186-1205, (2011)
  2. M. Fedele, F. Unguendoli, Rigorous Results on the Bipartite Mean-Field Model, Journal of Physics A: Mathematical and Theoretical, vol.45, N. 38, pag. 385001, (2012)
  3. M. Fedele, C. Vernia, P. Contucci, Inverse problem robustness for multi-species mean field models, preprint (2012); arXiv:1211.0465, submitted to Journal of Physics A: Mathematical and Theoretical

Conferences, schools, other events

  • Talk “Inverse problem for multispecies mean-field models”
    at Summer School in Probability 2012
    Bologna, Italy, 3-7 September 2012


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