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Stein's Method Applied to Preferential Attachment Graphs

Donderwinkel, S.A. (2016) Stein's Method Applied to Preferential Attachment Graphs. Bachelor's Thesis, Mathematics.

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Abstract

In probability and statistics, distributional limit theorems are used frequently. Stein’s method is a method to quantify the error in distributional convergence and determine the distance between the distribution of different random variables. In this thesis, Stein’s method is illustrated for different distributions. Up next, preferential attachment graphs are introduced. This is a type of random graphs in which vertices are added one by one and then connect to another vertex or itself with a probability proportional to the degree of the vertices. These graphs are also called ’rich-get-richer’-models. Stein’s method for the negative binomial distribution is then applied to illustrate rates of convergence for the total variation distance between the distribution of the degree of a randomly chosen vertex and an appropriate distribution as the number of vertices tends to infinity. Furthermore, power-law behaviour in preferential attachment graphs is shown.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:25
Last Modified: 15 Feb 2018 08:25
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/14579

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