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

TL;DR

This study applies Random Matrix Theory to analyze the eigenvalue spacing of temperature data from Meghalaya, revealing weak correlations among grid points through Brody distribution fitting.

Contribution

It introduces the use of RMT to analyze temperature eigenvalue statistics in Meghalaya, highlighting weak eigenvalue repulsion and correlation.

Findings

Eigenvalue spacing follows Brody distribution at β=0.045

Weak eigenvalue repulsion indicates low correlation among temperature grids

RMT effectively characterizes temperature data eigenvalue statistics

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.