Tagged particles and size-biased dynamics in mean-field interacting particle systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915824819765248 |
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| author | Koutsimpela, Angeliki Grosskinsky, Stefan |
| author_facet | Koutsimpela, Angeliki Grosskinsky, Stefan |
| contents | We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the occupation number on the tagged particle site converges to a time-inhomogeneous Markov process with non-linear master equation given by the law of large numbers of size-biased empirical measures. The latter are important in recent efforts to understand the dynamics of condensation in interacting particle systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tagged particles and size-biased dynamics in mean-field interacting particle systems Koutsimpela, Angeliki Grosskinsky, Stefan Probability Statistical Mechanics We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the occupation number on the tagged particle site converges to a time-inhomogeneous Markov process with non-linear master equation given by the law of large numbers of size-biased empirical measures. The latter are important in recent efforts to understand the dynamics of condensation in interacting particle systems. |
| title | Tagged particles and size-biased dynamics in mean-field interacting particle systems |
| topic | Probability Statistical Mechanics |
| url | https://arxiv.org/abs/2403.18179 |