1994/02/01 by P. C. Fishburn, James A. Reeds · 52 citations
Physics and Astronomy · Mathematics · #Quantum Mechanics and Applications #Benford’s Law and Fraud Detection #Analytic Number Theory Research #Mathematics #Combinatorics #Constant (computer programming) #Diagonal #Series (stratigraphy) #Yield (engineering) #Root (linguistics) #Discrete mathematics #Geometry #Physics
paper · doi:10.1137/s0895480191219350
published in SIAM Journal on Discrete Mathematics 7(1), 48-56 (Society for Industrial and Applied Mathematics)
openalex publication_date 1994/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
B. S. Tsirelson showed that comparisons between probabilities in “classical” physics and probabilities in quantum mechanics yield discrepancy measures Kn for finite n × n real matrices that approach Grothendieck’s constant KG as n gets large. It is known that K2 = K3 = √(2) and that KG ≥ π /2 = 1.57 ⋯ , but examples of n × n matrices for specified n that demonstrate Kn > √(2) have eluded researchers. A series of elementary examples are provided, which yield lower bounds on Kk ( k - 1 ) that approach 3/2 as k gets large. A uniform change along the main diagonal of our basic example shows that K20 \geqq = 10/7 = 1.42 ⋯ .