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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2508.18544 |
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| _version_ | 1866918130602737664 |
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| author | Vanni, Fabio Lambert, David |
| author_facet | Vanni, Fabio Lambert, David |
| contents | We model human mobility as a combinatorial allocation process, treating trips as distinguishable balls assigned to location-bins and generating origin-destination (OD) networks. From this analogy, we construct a unified three-scale framework, enumerative, probabilistic, and continuum graphon ensembles, and prove a renormalization theorem showing that, in the large sparse regime, these representations converge to a universal mixed-Poisson law. The framework yields compact formulas for key mobility observables, including destination occupancy, vacancy of unvisited sites, coverage (a stopping-time extension of the coupon collector problem), and overflow beyond finite capacities. Simulations with gravity-like kernels, calibrated on empirical OD data, closely match the asymptotic predictions. By connecting exact combinatorial models with continuum analysis, the results offer a principled toolkit for synthetic network generation, congestion assessment, and the design of sustainable urban mobility policies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18544 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Urn Modeling of Random Graphs Across Granularity Scales: A Framework for Origin-Destination Human Mobility Networks Vanni, Fabio Lambert, David Physics and Society Social and Information Networks 05C80, 60C05, 90B20, 91D10 We model human mobility as a combinatorial allocation process, treating trips as distinguishable balls assigned to location-bins and generating origin-destination (OD) networks. From this analogy, we construct a unified three-scale framework, enumerative, probabilistic, and continuum graphon ensembles, and prove a renormalization theorem showing that, in the large sparse regime, these representations converge to a universal mixed-Poisson law. The framework yields compact formulas for key mobility observables, including destination occupancy, vacancy of unvisited sites, coverage (a stopping-time extension of the coupon collector problem), and overflow beyond finite capacities. Simulations with gravity-like kernels, calibrated on empirical OD data, closely match the asymptotic predictions. By connecting exact combinatorial models with continuum analysis, the results offer a principled toolkit for synthetic network generation, congestion assessment, and the design of sustainable urban mobility policies. |
| title | Urn Modeling of Random Graphs Across Granularity Scales: A Framework for Origin-Destination Human Mobility Networks |
| topic | Physics and Society Social and Information Networks 05C80, 60C05, 90B20, 91D10 |
| url | https://arxiv.org/abs/2508.18544 |