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Scale-Free First Return Probability An Extensive Investigation

Journal: International Journal of Scientific & Technology Research (Vol.2, No. 4)

Publication Date:

Authors : ; ;

Page : 113-120

Keywords : Index Terms - random walk; gamblers ruin; first return time; nodes; links; hubs; preferential attachment rule; power-law degree distribution; fat tail; cumulative distribution.;

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Abstract

Abstract - We flip a coin and it is head with a probability p 12 purpose and tail with a probability q 1 - p 12. Consider if the coin land head we gain a dollar and if it is tail we lose a dollar. The game continues until a gambler who started with a finite playing this fair game go broke-known as the gamblers ruin problem. Also in the context of the random walk problem if one assumes that t denote the time at which the walker starting at the origin return to the origin. The purpose of this paper is to verify the theoretical prediction that the probability of the walker returns to the origin for the first time decay following the power law Ft t-32682602. In addition we show that it has fat tail which is reminiscent of the power law degree distribution of the scale free complex network as predicted by the Barabasi-Albert Model.

Last modified: 2013-08-10 23:33:59