Scaling limit of the cluster size distribution for the random current measure on the complete graph
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913539587833856 |
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| author | Krachun, Dmitrii Panagiotis, Christoforos Panis, Romain |
| author_facet | Krachun, Dmitrii Panagiotis, Christoforos Panis, Romain |
| contents | We study the percolation configuration arising from the random current representation of the near-critical Ising model on the complete graph. We compute the scaling limit of the cluster size distribution for an arbitrary set of sources in the single and the double current measures. As a byproduct, we compute the tangling probabilities recently introduced by Gunaratnam, Panagiotis, Panis, and Severo in [GPPS22]. This provides a new perspective on the switching lemma for the $φ^4$ model introduced in the same paper: in the Gaussian limit we recover Wick's law, while in the Ising limit we recover the corresponding tool for the Ising model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02087 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Scaling limit of the cluster size distribution for the random current measure on the complete graph Krachun, Dmitrii Panagiotis, Christoforos Panis, Romain Probability Mathematical Physics Combinatorics 60K35, 82B27, 82B43, 05C80 We study the percolation configuration arising from the random current representation of the near-critical Ising model on the complete graph. We compute the scaling limit of the cluster size distribution for an arbitrary set of sources in the single and the double current measures. As a byproduct, we compute the tangling probabilities recently introduced by Gunaratnam, Panagiotis, Panis, and Severo in [GPPS22]. This provides a new perspective on the switching lemma for the $φ^4$ model introduced in the same paper: in the Gaussian limit we recover Wick's law, while in the Ising limit we recover the corresponding tool for the Ising model. |
| title | Scaling limit of the cluster size distribution for the random current measure on the complete graph |
| topic | Probability Mathematical Physics Combinatorics 60K35, 82B27, 82B43, 05C80 |
| url | https://arxiv.org/abs/2310.02087 |