2024/05/14 by Vincent Viau, Viau, Vincent
Mathematics · #60J76 60J25 05C80 60J90 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2405.08664
openalex publication_date 2024/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a variant of the classical Erdős-Rényi random graph, where components with surplus are slowed down to prevent the apparition of complex components. The sizes of the components of this process undergo a similar phase transition to that of the classical model, and in the critical window the scaling limit of the sizes of the components is a "frozen" version of Aldous' multiplicative coalescent [2]. The aim of this article is to describe the long time asymptotics in the critical window for the total number of vertices which belong to a component with surplus.