Linear-in-M Nonzero Support for FEM Coupling Vectors w_k

Verifying that min_k |w_k|_0 >= cM for a universal constant c > 0, with implications for anti-concentration and diversity bounds.

c >= 0.67
Estimated Universal Constant
0.833
Asymptotic Ratio (M -> inf)
11.3x
Anti-Concentration Improvement at M=256
16x
Max Diversity Bound Improvement

Support Ratio min|w_k|_0 / M vs. Grid Size M

Minimum Support Scaling

The minimum support scales linearly with M, confirming the conjecture. The ratio stabilizes around 0.75-0.83, well above zero. The asymptotic fit (ratio = 0.833 + 0.703/M) shows convergence to approximately 0.833.

Support Scaling Data

MMin SupportRatio / MMean Support
441.0004.0
860.7507.4
16120.75014.9
32240.75030.3
64440.68861.7
128860.672124.5
2561780.695250.1
Linear Support for FEM Coupling Vectors — Computational Study