Sökning: L773:0066 2216 OR L773:1730 6272 >
Statistical mechani...
Statistical mechanics of interpolation nodes, pluripotential theory and complex geometry
-
- Berman, Robert, 1976 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
-
(creator_code:org_t)
- 2019
- 2019
- Engelska.
-
Ingår i: Annales Polonici Mathematici. - : Institute of Mathematics, Polish Academy of Sciences. - 0066-2216 .- 1730-6272. ; 123:1, s. 71-153
- Relaterad länk:
-
http://arxiv.org/pdf...
-
visa fler...
-
https://gup.ub.gu.se...
-
https://doi.org/10.4...
-
https://research.cha...
-
visa färre...
Abstract
Ämnesord
Stäng
- This is mainly a survey, explaining how the probabilistic (statistical mechanical) construction of Kahler-Einstein metrics on compact complex manifolds, introduced in a series of works by the author, naturally arises from classical approximation and interpolation problems in C-n. A fair amount of background material is included. Along the way the results are generalized to the non-compact setting of C-n. This yields a probabilistic construction of Kahler solutions to Einstein's equations in C-n, with cosmological constant -beta, from a gas of interpolation nodes in equilibrium at positive inverse temperature beta. In the infinite temperature limit, beta -> 0, solutions to the Calabi-Yau equation are obtained. In the opposite zero temperature case the results may be interpreted as "transcendental" analogs of classical asymptotics for orthogonal polynomials, with the inverse temperature beta playing the role of the degree of a polynomial.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- pluricomplex Green functions
- complex Monge-Ampere operators
- point
- processes
- large deviations
- monge-ampere equations
- equilibrium measures
- evolution-equations
- dirichlet problem
- large deviations
- bergman kernels
- gibbs measures
- fekete points
- monte-carlo
- kahler
- large deviations
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
Hitta via bibliotek
Till lärosätets databas