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Cross-Correlation in cricket data and RMT

Abstract

We analyze cross-correlation between runs scored over a time interval in cricket matches of different teams using methods of random matrix theory (RMT). We obtain an ensemble of cross-correlation matrices CC from runs scored by eight cricket playing nations for (i) test cricket from 1877 -2014 (ii)one-day internationals from 1971 -2014 and (iii) seven teams participating in the Indian Premier league T20 format (2008-2014) respectively. We find that a majority of the eigenvalues of C fall within the bounds of random matrices having joint probability distribution P(x1...,xn)=CNβj<kw(xj)xjxkβP(x_1...,x_n)=C_{N \beta} \, \prod_{j<k}w(x_j)| x_j-x_k |^\beta where w(x)=xNβaexp(Nβbx)w(x)=x^{N\beta a}\exp(-N\beta b x) and β\beta is the Dyson parameter. The corresponding level density gives Marchenko-Pastur (MP) distribution while fluctuations of every participating team agrees with the universal behavior of Gaussian Unitary Ensemble (GUE). We analyze the components of the deviating eigenvalues and find that the largest eigenvalue corresponds to an influence common to all matches played during these periods.Comment: 12 pages, 6 figure

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