Switching diffusivity selects Pareto tail exponent in random growth with redistribution

@misc{arutkin2026switching,
  title = {{Switching diffusivity selects Pareto tail exponent in random growth with redistribution}},
  author = {Maxence Arutkin and Alexandre Vallée},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.19464},
  eprint = {2605.19464},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.19464},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Switching diffusivity selects Pareto tail exponent in random growth with redistribution
AU  - Maxence Arutkin
AU  - Alexandre Vallée
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2605.19464
UR  - https://arxiv.org/abs/2605.19464
AB  - Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-Mézard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes, where volatility (diffusivity) is often fluctuating. We replace the constant noise intensity by a switching diffusivity and ask how these fluctuations select the Pareto stationary tail. For a geometric Brownian motion with switching diffusivity, the long-time Gaussian limit holds when the redraw law has finite mean and variance. The asymptotic variance retains a contribution from diffusivity persistence. With redistribution and a general redraw law, the stationary large-wealth problem is characterized by a spectral condition for admissible algebraic modes. For a two-state diffusivity, an exact tail analysis gives a Pareto exponent interpolating between the high-diffusivity slow-refresh limit and the mean-diffusivity fast-refresh Bouchaud-Mézard limit.
ER  -