Eigen Value Statistics of Long-Term Monthly Average Temperature of Meghalaya, India

Abstract

We use Random Matrix Theory (RMT) to describe the eigenvalue spacing of Meghalaya's historical monthly average temperature ($T_{avg}$) in grids. For that, the Nearest Neighbor Spacings ($S_i$) of the eigenvalues of the correlation matrices were found out for 1428 consecutive eigenvalue pair differences. It is found that the distribution of $S_i$ follows Brody distribution at a correlation value of $\beta=0.045$. This value of $\beta(0.045)$ indicates weak repulsion among the eigenvalues as it is closer to Poisson fluctuations, meaning there is a weak correlation among the grids.