AN ELEMENTARY APPROACH TO COMPONENT SIZES IN CRITICAL RANDOM GRAPHS

Umberto de Ambroggio

doi:10.1017/jpr.2022.13

AN ELEMENTARY APPROACH TO COMPONENT SIZES IN CRITICAL RANDOM GRAPHS

Umberto de Ambroggio

Centre for Mathematical Biology

Research output: Contribution to journal › Article › peer-review

Abstract

In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models of random graphs when considered at criticality. Specifically, we apply our method to a model of a random intersection graph, a random graph obtained through p-bond percolation on a general d-regular graph, and a model of an inhomogeneous random graph.

Original language	English
Pages (from-to)	1228-1242
Number of pages	15
Journal	Journal of Applied Probability
Volume	59
Issue number	4
Early online date	11 Nov 2022
DOIs	https://doi.org/10.1017/jpr.2022.13
Publication status	Published - 24 Dec 2022

Keywords

ballot theorem
Random walk

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

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10.1017/jpr.2022.13

Cite this

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abstract = "In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models of random graphs when considered at criticality. Specifically, we apply our method to a model of a random intersection graph, a random graph obtained through p-bond percolation on a general d-regular graph, and a model of an inhomogeneous random graph.",

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AB - In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models of random graphs when considered at criticality. Specifically, we apply our method to a model of a random intersection graph, a random graph obtained through p-bond percolation on a general d-regular graph, and a model of an inhomogeneous random graph.

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AN ELEMENTARY APPROACH TO COMPONENT SIZES IN CRITICAL RANDOM GRAPHS

Abstract

Keywords

ASJC Scopus subject areas

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