A mean-field theory for heterogeneous random growth with redistribution
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918381024706560 |
|---|---|
| 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 |