Nearest-neighbor radii converge almost surely and obey local-dimension moment bounds under polynomial and geometric mixing dependence.
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Consistent rank correlation matrices in the proportional high-dimensional regime converge in spectral distribution to the semicircle law.
The attainable (ξ, ρ) region is a convex set with boundary from novel diagonal-band copulas; ξ ≤ |ρ| holds under stochastic monotonicity and the maximum of ρ − ξ equals 0.4.
Extends the Chatterjee-Spearman max-type test to symmetric form with derived null distribution, proves asymptotic independence from Kendall's tau and quadrant correlation, and explores multivariate cases with simulation evidence of improved power.
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The exact region and an inequality between Chatterjee's and Spearman's rank correlations
The attainable (ξ, ρ) region is a convex set with boundary from novel diagonal-band copulas; ξ ≤ |ρ| holds under stochastic monotonicity and the maximum of ρ − ξ equals 0.4.