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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, UniversitÃ degli Studi di Bologna

Research project:*Statistical mechanics models for the study of interactinmg populations.*Supervisor: P. Contucci.

#### Publications, preprints, other works

- 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) - 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) - 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