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Spectral analysis of large dimensional Chatterjee's rank correlation matrix
Zhaorui Dong, Fang Han, Jianfeng Yao
https://arxiv.org/abs/2510.07262 https://

Spectral analysis of large dimensional Chatterjee's rank correlation matrix
This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector with independent continuous components. We show that the empirical spectral distribution of its symmetrized version converges to the semicircle law, and thus providing the first example of a large correlation matrix deviating from the Marchenko-Pastur law that governs those of Pearson, Kendall, and Spearman. We further e…

The origin of the galaxy size-stellar metallicity relation: A semi-analytical perspective
Kai Wang (Durham University)
https://arxiv.org/abs/2510.02573 https://

The origin of the galaxy size-stellar metallicity relation: A semi-analytical perspective
Stellar metallicity encodes the integrated effects of gas inflow, star formation, and feedback-driven outflow, yet its connection to galaxy structure remains poorly understood. Using SDSS-IV MaNGA, we present the direct observational evidence that, at fixed stellar mass, smaller central galaxies are systematically more metal-rich, with a Spearman's rank correlation coefficient reaching $R_{\rm s}\approx -0.4$. The semi-analytical model L-GALAXIES reproduces this anti-correlation, albeit with a …