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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.21097 |
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| _version_ | 1866917292048121856 |
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| author | Cifani, Paolo Flandoli, Franco Marino, Lorenzo |
| author_facet | Cifani, Paolo Flandoli, Franco Marino, Lorenzo |
| contents | In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric $α$-stable-like process. Motivated by recent works showing that complex small-scale spatial structures often lead to Brownian dispersion, we study if this principle persists when the driving noise exhibits heavy-tailed jump statistics. Our numerical results show a clear dichotomy linked with the tail behaviour of the noise. When considering standard $α$-stable processes, very large jumps survive the interaction with the spatial complexity and yield anomalous, super-diffusive transport. In contrast, when the $α$-stable noise is either truncated or exponentially tempered, suppressing extremely long jumps, the transport undergoes a transition to a classical diffusive regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21097 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Anomalous diffusion properties of stochastic transport by heavy-tailed jump processes Cifani, Paolo Flandoli, Franco Marino, Lorenzo Mathematical Physics In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric $α$-stable-like process. Motivated by recent works showing that complex small-scale spatial structures often lead to Brownian dispersion, we study if this principle persists when the driving noise exhibits heavy-tailed jump statistics. Our numerical results show a clear dichotomy linked with the tail behaviour of the noise. When considering standard $α$-stable processes, very large jumps survive the interaction with the spatial complexity and yield anomalous, super-diffusive transport. In contrast, when the $α$-stable noise is either truncated or exponentially tempered, suppressing extremely long jumps, the transport undergoes a transition to a classical diffusive regime. |
| title | Anomalous diffusion properties of stochastic transport by heavy-tailed jump processes |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2602.21097 |