New Lower and Upper Bounds for the Grothendieck Constant
- View PDF HTML (experimental) Abstract:We establish new bounds on the Grothendieck constant $K_G$: \[ \frac{6\pi}{11} \le K_G \le \frac{\pi}{2\log(1+\sqrt2)} - 10^{-4}.
- \] Methodologically, our lower bound approach differs from previous works by establishing limitations on the asymptotically optimal Krivine schemes, rather than giving explicit constructions of gap instances.
- Our upper bound is obtained by proposing and analyzing the first asymptotic construction of rounding schemes, whereas previous works only consider low-dimensional schemes.
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- View PDF HTML (experimental) Abstract:We establish new bounds on the Grothendieck constant $K_G$: \[ \frac{6\pi}{11} \le K_G \le \frac{\pi}{2\log(1+\sqrt2)} - 10^{-4}.
- \] Methodologically, our lower bound approach differs from previous works by establishing limitations on the asymptotically optimal Krivine schemes, rather than giving explicit constructions of gap instances.
- Our upper bound is obtained by proposing and analyzing the first asymptotic construction of rounding schemes, whereas previous works only consider low-dimensional schemes.
Sources: Arxiv