A new preprint in applied probability

Dr Angelica Pachon, Maths


Dr Angelica Pachon has recently uploaded a paper to the "Mathematics Preprint Archive". This is a joint work with Dr Umberto De Ambroggio of Bath University. 


Dr Angelica Pachon - Upper bounds for the largest components in critical inhomogeneous random graphs


Umberto visited USW in the Autumn of 2021 as part of the Faculty RIS project "Complex Networks and Data Science", University of South Wales, and the last part of this paper grew out of research undertaken during his visit.


In this paper, entitled "Upper bounds for the largest components in critical inhomogeneous random graphs", we consider the Norros-Reittu random graph. In this graph edges are independent, but edge probabilities are constrained by vertex weights. 


We use probabilistic arguments based on martingales to analyse the component sizes in this model when considered at criticality. In particular, we obtain stronger upper bounds than those in published literature for the probability of observing unusually large maximal clusters. 


Further, we simplify the arguments needed to derive polynomial upper bounds for the probability of observing unusually small maximal components. 


The paper may be found at: https://arxiv.org/abs/2012.09001