Abstract
We consider a class of dynamic random graphs known as preferential attachment models, where the probability that a new vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known that the distribution of a uniformly chosen vertex converges to a limiting distribution. Depending on the parameters, the tail of the limiting distribution may behave like a power law or a stretched exponential. Using Stein's method we provide rates of convergence to zero of the total variation distance between the finite distribution and its limit. Our proof uses the fact that the limiting distribution is the stationary distribution of a Markov chain together with the generator method of Barbour.
Original language  English 

Pages (fromto)  808830 
Number of pages  23 
Journal  Random Structures and Algorithms 
Volume  55 
Issue number  4 
Early online date  2 Apr 2019 
DOIs  
Publication status  Published  1 Dec 2019 
Keywords
 random graphs
 Preferential attachment
 Stein's method
 coupling
 rates of convergence
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Profiles

Marcel Ortgiese
 Department of Mathematical Sciences  Senior Lecturer
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
 Probability Laboratory at Bath
Person: Research & Teaching