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Partial Localization and Multifractality in Heterogeneous Population Growth with Resetting

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  • Maximilien Bernard
  • Giuseppe Del Vecchio Del Vecchio
  • Jean-Philippe Bouchaud
  • Pierre Le Doussal

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

Suggested Citation

  • Maximilien Bernard & Giuseppe Del Vecchio Del Vecchio & Jean-Philippe Bouchaud & Pierre Le Doussal, 2026. "Partial Localization and Multifractality in Heterogeneous Population Growth with Resetting," Papers 2610.22038, arXiv.org.
    • Handle: RePEc:arx:papers:2610.22038
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    File URL: https://arxiv.org/pdf/2610.22038
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