Partial Localization and Multifractality in Heterogeneous Population Growth with Resetting
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 Nu⋆ favorable candidates, with 0<u⋆<1. We derive the corresponding growth rate from a saddle point analysis, and show that the averaged stationary fractions display multifractal behavior.
Related
- From Individual Trajectories to Population Densities: Weak-Form Inference of Heterogeneous Growth Laws
- Biophysical resetting of specialization drives evolutionary diversification of a metabolic network
- Slow-fast dynamics of the McKean model with stochastic resetting and diffusion
- Rapid phase resetting of Aedes aegypti circadian rhythms by transient alterations in light exposure
- Revisiting genome-guided RNA localization in bacteria
BibTeX
@misc{bernard2026partial,
title = {{Partial Localization and Multifractality in Heterogeneous Population Growth with Resetting}},
author = {Maximilien Bernard and Giuseppe Del Vecchio Del Vecchio and Jean-Philippe Bouchaud and Pierre Le Doussal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22038},
eprint = {2610.22038},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22038},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Partial Localization and Multifractality in Heterogeneous Population Growth with Resetting
AU - Maximilien Bernard
AU - Giuseppe Del Vecchio Del Vecchio
AU - Jean-Philippe Bouchaud
AU - Pierre Le Doussal
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22038
UR - https://arxiv.org/abs/2610.22038
AB - 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^⋆ favorable candidates, with 0<u^⋆<1. We derive the corresponding growth rate from a saddle point analysis, and show that the averaged stationary fractions display multifractal behavior.
ER -