Statistical mechanics of interpolation nodes, pluripotential theory and complex geometry

DOI10.4064/ap180925-4-7zbMath1452.32040arXiv1810.06939OpenAlexW2981934802MaRDI QIDQ5207246

Robert J. Berman

Publication date: 19 December 2019

Published in: Annales Polonici Mathematici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.06939

zbMATH Keywords

large deviationspoint processescomplex Monge-Ampère operatorspluricomplex Green functions

Mathematics Subject Classification ID

Large deviations (60F10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Complex Monge-Ampère operators (32W20) Plurisubharmonic extremal functions, pluricomplex Green functions (32U35)

Related Items

Coulomb and Riesz gases: The known and the unknown ⋮ Kähler-Einstein metrics and Archimedean zeta functions ⋮ Emergent complex geometry ⋮ Priors leading to well-behaved Coulomb and Riesz gases versus zeroth-order phase transitions -- a potential-theoretic characterization

Cites Work

• Large deviation principles and complete equivalence and nonequivalence results for pure and mixed ensembles
• Kähler-Einstein metrics with edge singularities
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equidistribution estimates for Fekete points on complex manifolds
• K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
• Kiselman's principle, the Dirichlet problem for the Monge-Ampère equation, and rooftop obstacle problems
• A variational approach to complex Monge-Ampère equations
• Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties
• Geometry in the tropical limit
• First-order global asymptotics for confined particles with singular pair repulsion
• Kähler-Einstein metrics emerging from free fermions and statistical mechanics
• Degenerate complex Monge-Ampère equations
• Monge-Ampère equations in big cohomology classes
• Fekete points and convergence towards equilibrium measures on complex manifolds
• \(L^ p\) and mean value properties of subharmonic functions on Riemannian manifolds
• Réduction du cas positif de l'équation de Monge-Ampère sur les variétés Kählériennes compactes à la démonstration d'une inégalité
• A new capacity for plurisubharmonic functions
• Intrinsic capacities on compact Kähler manifolds
• Entropy, large deviations, and statistical mechanics.
• The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles
• Uniform approximation by discrete least squares polynomials
• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kähler metrics
• Determinantal processes and independence
• Growth of balls of holomorphic sections and energy at equilibrium
• Asymptotics for Christoffel functions of planar measures
• From random matrices to random analytic functions
• Large deviations techniques and applications.
• A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
• A Monte Carlo algorithm for free and coaxial ring extremal states of the vortex \(N\)-body problem on a sphere
• Rigorous analysis of discontinuous phase transitions via mean-field bounds
• Extremal systems of points and numerical integration on the sphere
• On the hydrodynamic limit of Ginzburg-Landau vortices.
• Asymptotic distribution of nodes for near-optimal polynomial interpolation on certain curves in \(\mathbb{R}^2\)
• Dynamics of a planar Coulomb gas
• Propagation of chaos, Wasserstein gradient flows and toric Kähler-Einstein metrics
• Stochastic particle approximation of the Keller-Segel equation and two-dimensional generalization of Bessel processes
• Energy of the Coulomb gas on the sphere at low temperature
• Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds
• Large deviations for Gibbs measures with singular Hamiltonians and emergence of Kähler-Einstein metrics
• Coulomb gases and Ginzburg-Landau vortices
• Large deviations for configurations generated by Gibbs distributions with energy functionals consisting of singular interaction and weakly confining potentials
• Mean field limit for Coulomb-type flows
• The high temperature crossover for general 2D Coulomb gases
• Plurisubharmonic envelopes and supersolutions
• A large deviation principle for empirical measures on Polish spaces: application to singular Gibbs measures on manifolds
• Complexity of Bezout's theorem. III: Condition number and packing
• On large deviations for Gibbs measures, mean energy and gamma-convergence
• A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics
• A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators
• Determinantal point processes and fermions on complex manifolds: large deviations and bosonization
• Zeros of random polynomials on \(\mathbb C^m\)
• Monte Carlo strategies in scientific computing.
• From Monge-Ampère equations to envelopes and geodesic rays in the zero temperature limit
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Degenerate complex Hessian equations on compact Kahler manifolds
• Corrigendum: Viscosity Solutions to Complex Monge-Ampère Equations
• Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra
• Viscosity solutions to degenerate complex monge-ampère equations
• Onsager and the theory of hydrodynamic turbulence
• Monge-Ampere Measures Associated to Extremal Plurisubharmonic Functions in C n
• Bergman kernels for weighted polynomials and weighted equilibrium measures of $\mathbb{C}^{n}$
• The importance of the Selberg integral
• A gradient flow approach to an evolution problem arising in superconductivity
• Bergman kernels and equilibrium measures for line bundles over projective manifolds
• The Complex Equilibrium Measure of a Symmetric Convex Set in R n
• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
• Families of polynomials and determining measures
• Extremal plurisubharmonic functions in $C^N$
• The Regularity of Mappings with a Convex Potential
• Экстремальные плюрисубгармонические функции, ортогональные многочлены и теорема Бернштейна-Уолша для аналитических функций многих комплексных переменных
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Statistical mechanics of classical particles with logarithmic interactions
• Singularities of Pairs
• Indicators for plurisubharmonic functions of logarithmic growth
• Large deviation principle for some beta ensembles
• Pluripotential theory and convex bodies
• Equidistribution and $\beta$ ensembles
• Large deviations from the mckean-vlasov limit for weakly interacting diffusions
• Matrix models for beta ensembles
• A mean-field model of superconducting vortices
• Kähler–Einstein metrics, canonical random point processes and birational geometry
• Stability of algebraic varieties and Kähler geometry
• Equidistribution speed for Fekete points associated with an ample line bundle
• Bernstein-Markov: a survey
• Pluripotential energy and large deviation
• Permanental Point Processes on Real Tori, Theta Functions and Monge–Ampère Equations