Hyperscaling of spatial fluctuations constrains the development of urban populations
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915909384273920 |
|---|---|
| author | Merbis, Wout Santos, Fernando A. N. Armas, Jay Pijpers, Frank Lees, Mike |
| author_facet | Merbis, Wout Santos, Fernando A. N. Armas, Jay Pijpers, Frank Lees, Mike |
| contents | Urban populations exhibit fractal organization and systematic scaling regularities, yet the scaling exponents reported across cities vary substantially, challenging existing theory. Using 100~m gridded population maps for 477 urban areas spanning the Netherlands (2000--2023) and major world cities (1975--2020), we recursively coarse-grain each city and quantify how the mean and variance of inhabitants in square grid cells of side length $\ell$ scale with $\ell$. This yields two exponents, $β$ from $\langle N_\ell\rangle\sim \ell^β$ and $γ$ from $\mathrm{Var}(N_\ell)\sim \ell^γ$, where in the small-$\ell$ limit $β$ equals the planar fractal dimension of populated space. Across cities within a given year, $γ$ depends linearly on $β$. Compiling $>$10,000 exponent estimates over five decades shows that this hyperscaling relation is robust yet non-universal: its slope and intercept vary across continents and drift systematically in time, trending toward the limiting form $γ\simeq 2+β$. A mean-field (independent-cell) argument predicts a quadratic mean--variance mapping and cannot reproduce the observed $β$--$γ$ dependence, implying strong spatial correlations. We derive a correlation-aware variance decomposition in which $γ$ is controlled by a correlation dimension $D_c$; in the correlation-dominated regime $γ=2+D_c$. If large maturing cities, as are the ones selected in our dataset, evolve to effective monofractal ($D_c\simeq β$) cities, the asymptotic prediction becomes $γ\simeq 2+β$, consistent with the observed temporal drift. This interdependence links urban form and fluctuations, constrains mechanistic growth models, and implies scaling predictions for spatial indicators built from local means and variances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01969 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hyperscaling of spatial fluctuations constrains the development of urban populations Merbis, Wout Santos, Fernando A. N. Armas, Jay Pijpers, Frank Lees, Mike Physics and Society Statistical Mechanics Adaptation and Self-Organizing Systems Urban populations exhibit fractal organization and systematic scaling regularities, yet the scaling exponents reported across cities vary substantially, challenging existing theory. Using 100~m gridded population maps for 477 urban areas spanning the Netherlands (2000--2023) and major world cities (1975--2020), we recursively coarse-grain each city and quantify how the mean and variance of inhabitants in square grid cells of side length $\ell$ scale with $\ell$. This yields two exponents, $β$ from $\langle N_\ell\rangle\sim \ell^β$ and $γ$ from $\mathrm{Var}(N_\ell)\sim \ell^γ$, where in the small-$\ell$ limit $β$ equals the planar fractal dimension of populated space. Across cities within a given year, $γ$ depends linearly on $β$. Compiling $>$10,000 exponent estimates over five decades shows that this hyperscaling relation is robust yet non-universal: its slope and intercept vary across continents and drift systematically in time, trending toward the limiting form $γ\simeq 2+β$. A mean-field (independent-cell) argument predicts a quadratic mean--variance mapping and cannot reproduce the observed $β$--$γ$ dependence, implying strong spatial correlations. We derive a correlation-aware variance decomposition in which $γ$ is controlled by a correlation dimension $D_c$; in the correlation-dominated regime $γ=2+D_c$. If large maturing cities, as are the ones selected in our dataset, evolve to effective monofractal ($D_c\simeq β$) cities, the asymptotic prediction becomes $γ\simeq 2+β$, consistent with the observed temporal drift. This interdependence links urban form and fluctuations, constrains mechanistic growth models, and implies scaling predictions for spatial indicators built from local means and variances. |
| title | Hyperscaling of spatial fluctuations constrains the development of urban populations |
| topic | Physics and Society Statistical Mechanics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2604.01969 |