Year: 2026
Type: preprint
Abstract: We study a model of heterogeneous multiplicative growth with mean-field redistribution and independent local stochastic resetting. The model describes populations or wealth distributed over sites with quenched growth-rate heterogeneity, while resets represent random local extinction or bankruptcy events. At large redistribution or resetting rate, we find a delocalized phase and we compute the growth rate as well as the stationary distribution of the population of a given site. We show that reset-free growth episodes generate power-law stationary tails with site-dependent exponents. For weak resetting and redistribution, favorable sites can undergo long reset-free episodes and localize. This produces a partially localized phase, in which a finite fraction of the total population is carried by a small set of sites whose identity changes on an $O(1)$ time scale within a subextensive pool of $N^{u^\star}$ favorable candidates, with $0
Source: arXiv (Cornell University)
Institutions: Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, Université Paris-Saclay, École Normale Supérieure - PSL, Laboratoire de Physique Théorique et Modèles Statistiques, Laboratoire de Physique de l'Ecole Normale Supérieure, Capital Fund Management (France)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222411473