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The spherical ensem...
Abstract
Ämnesord
Stäng
- The spherical ensemble is a well-known ensemble of N repulsive points on the twodimensional sphere, which can realized in various ways (as a random matrix ensemble, a determinantal point process, a Coulomb gas, a Quantum Hall state...). Here we show that the spherical ensemble enjoys remarkable convergence properties from the point of view of numerical integration. More precisely, it is shown that the numerical integration rule corresponding to N nodes on the two-dimensional sphere sampled in the spherical ensemble is, with overwhelming probability, nearly a quasi-Monte-Carlo design in the sense of Brauchart-Saff-Sloan-Womersley for any smoothness parameter s = 2. The key ingredient is a new explicit sub-Gaussian concentration of measure inequality for the spherical ensemble.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Fysik -- Annan fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences -- Other Physics Topics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- Quasi-Monte-Carlo designs
- Coulomb gas
- Numerical integration
- Concentration of measure
- distributing points
- hecke operators
- coulomb gases
- bounds
- Mathematics
- Numerical integration
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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