Hydrodynamic limit for repeated averages on the complete graph
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910893008224256 |
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| author | Campos, Alberto M. Franco, Tertuliano Heydenreich, Markus Schrocke, Marcel |
| author_facet | Campos, Alberto M. Franco, Tertuliano Heydenreich, Markus Schrocke, Marcel |
| contents | We establish a hydrodynamical limit for the averaging process on the complete graph with N vertices, showing that, after a timescale of order N, the empirical distribution of opinions converges to a unique measure. Moreover, if the initial distribution is absolutely continuous concerning the Lebesgue measure, the limiting measure remains absolutely continuous and its density satisfies a non-diffusive differential equation, that resembles the Smoluchowski coagulation equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limit for repeated averages on the complete graph Campos, Alberto M. Franco, Tertuliano Heydenreich, Markus Schrocke, Marcel Probability 60K35, 82C22, 60K35, 35Q70, 37L05, 47J35 We establish a hydrodynamical limit for the averaging process on the complete graph with N vertices, showing that, after a timescale of order N, the empirical distribution of opinions converges to a unique measure. Moreover, if the initial distribution is absolutely continuous concerning the Lebesgue measure, the limiting measure remains absolutely continuous and its density satisfies a non-diffusive differential equation, that resembles the Smoluchowski coagulation equation. |
| title | Hydrodynamic limit for repeated averages on the complete graph |
| topic | Probability 60K35, 82C22, 60K35, 35Q70, 37L05, 47J35 |
| url | https://arxiv.org/abs/2503.19743 |