Near critical asymptotics in the Frozen Erdős-Rényi
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913350493929472 |
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| author | Viau, Vincent |
| author_facet | Viau, Vincent |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Near critical asymptotics in the Frozen Erdős-Rényi Viau, Vincent Probability 60J76 60J25 05C80 60J90 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. |
| title | Near critical asymptotics in the Frozen Erdős-Rényi |
| topic | Probability 60J76 60J25 05C80 60J90 |
| url | https://arxiv.org/abs/2405.08664 |