A mean-field theory for heterogeneous random growth with redistribution

Fuente: arXiv
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Auteurs principaux: Bernard, Maximilien, Bouchaud, Jean-Philippe, Doussal, Pierre Le
Format: Preprint
Publié: 2025
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author Bernard, Maximilien
Bouchaud, Jean-Philippe
Doussal, Pierre Le
author_facet Bernard, Maximilien
Bouchaud, Jean-Philippe
Doussal, Pierre Le
contents We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong enough to prevent localisation, i.e. extreme concentration on the fastest growing site. In the presence of an additional temporal noise in the growth rates, a third partially localised phase is predicted theoretically, using results from Derrida's Random Energy Model. Such temporal fluctuations mitigate concentration effects, but do not make them disappear. We discuss our results in the context of population growth and wealth inequalities.
format Preprint
id arxiv_https___arxiv_org_abs_2503_23189
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A mean-field theory for heterogeneous random growth with redistribution
Bernard, Maximilien
Bouchaud, Jean-Philippe
Doussal, Pierre Le
Disordered Systems and Neural Networks
Statistical Mechanics
General Economics
Economics
Probability
Populations and Evolution
We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong enough to prevent localisation, i.e. extreme concentration on the fastest growing site. In the presence of an additional temporal noise in the growth rates, a third partially localised phase is predicted theoretically, using results from Derrida's Random Energy Model. Such temporal fluctuations mitigate concentration effects, but do not make them disappear. We discuss our results in the context of population growth and wealth inequalities.
title A mean-field theory for heterogeneous random growth with redistribution
topic Disordered Systems and Neural Networks
Statistical Mechanics
General Economics
Economics
Probability
Populations and Evolution
url https://arxiv.org/abs/2503.23189