Scaling limit of the cluster size distribution for the random current measure on the complete graph

Autor:	Krachun, Dmitrii, Panagiotis, Christoforos, Panis, Romain
Rok vydání:	2023
Předmět:	Mathematics - Probability Mathematical Physics Mathematics - Combinatorics 60K35 82B27 82B43 05C80
Druh dokumentu:	Working Paper
Popis:	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 $\varphi^4$ 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. Comment: 25 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.02087 Zobrazit plný text záznamu View this record from Arxiv