Diffusing diffusivity selects Pareto tail exponent in random growth with redistribution
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| Format: | Preprint |
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2026
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| _version_ | 1866916025917767680 |
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| author | Arutkin, Maxence Vallée, Alexandre |
| author_facet | Arutkin, Maxence Vallée, Alexandre |
| contents | 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 diffusing diffusivity and ask how these fluctuations select the Pareto stationary tail. For a geometric Brownian motion with diffusing diffusivity, the effect is transient: log-returns show non-Gaussian short-time statistics but self-average to a Gaussian form at long times. With redistribution, the same persistence becomes stationary. Agents remaining in high-diffusivity states dominate rare large-wealth events, so the Pareto exponent is not obtained by replacing the diffusivity by its mean. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_19464 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diffusing diffusivity selects Pareto tail exponent in random growth with redistribution Arutkin, Maxence Vallée, Alexandre Disordered Systems and Neural Networks Statistical Mechanics 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 diffusing diffusivity and ask how these fluctuations select the Pareto stationary tail. For a geometric Brownian motion with diffusing diffusivity, the effect is transient: log-returns show non-Gaussian short-time statistics but self-average to a Gaussian form at long times. With redistribution, the same persistence becomes stationary. Agents remaining in high-diffusivity states dominate rare large-wealth events, so the Pareto exponent is not obtained by replacing the diffusivity by its mean. 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. |
| title | Diffusing diffusivity selects Pareto tail exponent in random growth with redistribution |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2605.19464 |