2016, 1, Monographs and research notes in mathematics, ISBN 1482210509, xix, 286

Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces...

Cauchy problem | Financial Mathematics | Differential Equations | Mathematical Analysis | Stochastic processes | Infinite dimensional Lie algebras | Stochastic differential equations

Cauchy problem | Financial Mathematics | Differential Equations | Mathematical Analysis | Stochastic processes | Infinite dimensional Lie algebras | Stochastic differential equations

Book

Living reviews in relativity, ISSN 1433-8351, 2008, Volume 11, Issue 1, pp. 1 - 87

... in Higher Dimensions Roberto Emparan Institució Catalana de Recerca i Estudis Avançats (ICREA) and Departament de F́ısica Fonamental, Universitat de Barcelona Marti...

Black String | Astrophysics and Astroparticles | Black Hole | Conformal Field Theory | Black Brane | Black Ring | Cosmology | Classical and Quantum Gravitation, Relativity Theory | Physics | SPACETIMES | SELF-DUALITY | SOLITON-SOLUTIONS | FIELD | FLAT SPACELIKE HYPERSURFACE | ADS X S | INFINITE NUMBER | EINSTEIN-MAXWELL-EQUATIONS | STRING THEORY | STATIONARY | PHYSICS, PARTICLES & FIELDS | Forats negres (Astronomia) | Supergravetat | Supergravity | Black holes (Astronomy) | Review | black holes | string theory | supergravity

Black String | Astrophysics and Astroparticles | Black Hole | Conformal Field Theory | Black Brane | Black Ring | Cosmology | Classical and Quantum Gravitation, Relativity Theory | Physics | SPACETIMES | SELF-DUALITY | SOLITON-SOLUTIONS | FIELD | FLAT SPACELIKE HYPERSURFACE | ADS X S | INFINITE NUMBER | EINSTEIN-MAXWELL-EQUATIONS | STRING THEORY | STATIONARY | PHYSICS, PARTICLES & FIELDS | Forats negres (Astronomia) | Supergravetat | Supergravity | Black holes (Astronomy) | Review | black holes | string theory | supergravity

Journal Article

Physical review. B, Condensed matter and materials physics, ISSN 1550-235X, 2015, Volume 91, Issue 12

We have studied the impact of nonlocal electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated...

PLAQUETTE | PHYSICS, CONDENSED MATTER | METAL-INSULATOR-TRANSITION | TEMPERATURE | HEISENBERG | INFINITE DIMENSIONS | ANTIFERROMAGNETISM | FERMION SYSTEMS | FERROMAGNETISM | PSEUDOGAP | MODEL | Physics - Strongly Correlated Electrons

PLAQUETTE | PHYSICS, CONDENSED MATTER | METAL-INSULATOR-TRANSITION | TEMPERATURE | HEISENBERG | INFINITE DIMENSIONS | ANTIFERROMAGNETISM | FERMION SYSTEMS | FERROMAGNETISM | PSEUDOGAP | MODEL | Physics - Strongly Correlated Electrons

Journal Article

Journal of computational physics, ISSN 0021-9991, 2016, Volume 304, Issue C, pp. 109 - 137

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying...

Infinite-dimensional inverse problems | Likelihood-informed subspace | Langevin SDE | Conditioned diffusion | Markov chain Monte Carlo | ERGODICITY | DIFFUSION LIMITS | LANGEVIN ALGORITHM | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STOCHASTIC NEWTON MCMC | INVERSE PROBLEMS | METROPOLIS ALGORITHM | Markov processes | Monte Carlo method | Differential equations | Reconstruction | Samplers | Inverse problems | Discretization | Mathematical analysis | Mathematical models | Proposals | likelihood-informed subspace | langevin SDE | MATHEMATICS AND COMPUTING | infinite-dimensional inverse problems | conditioned diffusion

Infinite-dimensional inverse problems | Likelihood-informed subspace | Langevin SDE | Conditioned diffusion | Markov chain Monte Carlo | ERGODICITY | DIFFUSION LIMITS | LANGEVIN ALGORITHM | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STOCHASTIC NEWTON MCMC | INVERSE PROBLEMS | METROPOLIS ALGORITHM | Markov processes | Monte Carlo method | Differential equations | Reconstruction | Samplers | Inverse problems | Discretization | Mathematical analysis | Mathematical models | Proposals | likelihood-informed subspace | langevin SDE | MATHEMATICS AND COMPUTING | infinite-dimensional inverse problems | conditioned diffusion

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2012, Volume 252, Issue 10, pp. 5832 - 5851

In this paper we consider quasilinear Keller–Segel type systems of two kinds in higher dimensions...

Infinite-time blowup | Chemotaxis | Finite-time blowup | MATHEMATICS | BOUNDEDNESS | Mathematics - Analysis of PDEs

Infinite-time blowup | Chemotaxis | Finite-time blowup | MATHEMATICS | BOUNDEDNESS | Mathematics - Analysis of PDEs

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 12/2014, Volume 24, Issue 6, pp. 2455 - 2490

We study the problem of sampling high and infinite dimensional target measures arising in applications such as conditioned diffusions and inverse problems. We...

Ergodic theory | Liapunov functions | Approximation | Inverse problems | Central limit theorem | Mathematical theorems | Random walk | Markov chains | Metropolitan areas | Density | spectral gaps | Markov chain Monte Carlo in infinite dimensions | Weak Harris theorem | Wasserstein spectral gaps | Random walk Metropolis | MCMC METHODS | SEMIGROUPS | RECURRENT MARKOV-CHAINS | INEQUALITIES | SPACES | INVERSE PROBLEMS | CONVERGENCE | STATISTICS & PROBABILITY | ERROR-BOUNDS | CHAIN MONTE-CARLO | CENTRAL-LIMIT-THEOREM | 65C40 | random walk Metropolis | 60B10 | L^{2}-spectral gaps | weak Harris theorem | 60J05 | 60J22

Ergodic theory | Liapunov functions | Approximation | Inverse problems | Central limit theorem | Mathematical theorems | Random walk | Markov chains | Metropolitan areas | Density | spectral gaps | Markov chain Monte Carlo in infinite dimensions | Weak Harris theorem | Wasserstein spectral gaps | Random walk Metropolis | MCMC METHODS | SEMIGROUPS | RECURRENT MARKOV-CHAINS | INEQUALITIES | SPACES | INVERSE PROBLEMS | CONVERGENCE | STATISTICS & PROBABILITY | ERROR-BOUNDS | CHAIN MONTE-CARLO | CENTRAL-LIMIT-THEOREM | 65C40 | random walk Metropolis | 60B10 | L^{2}-spectral gaps | weak Harris theorem | 60J05 | 60J22

Journal Article

7.
Full Text
Stochastic Cauchy Problems in Infinite Dimensions

: Generalized and Regularized Solutions

09/2018, Chapman & Hall/CRC Monographs and Research Notes in Mathematics, ISBN 1482210509, 286

Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces...

STMnetBASE | regularized semi-groups | SCI-TECHnetBASE | MATHnetBASE | regularization | Financial Mathematics | Gelfand–Shilov spaces | Hilbert spaces | Differential Equations | stochastic differential equations | Mathematical Analysis | Cauchy problem | semi-group and distribution methods | infinite-dimensional stochastic analysis | integral equations | white noise analysis

STMnetBASE | regularized semi-groups | SCI-TECHnetBASE | MATHnetBASE | regularization | Financial Mathematics | Gelfand–Shilov spaces | Hilbert spaces | Differential Equations | stochastic differential equations | Mathematical Analysis | Cauchy problem | semi-group and distribution methods | infinite-dimensional stochastic analysis | integral equations | white noise analysis

eBook

Theory of Computing Systems, ISSN 1432-4350, 11/2017, Volume 61, Issue 4, pp. 1288 - 1314

In this paper we derive several results which generalise the constructive dimension of (sets...

Hausdorff dimension | Super-martingales | Computer Science | Infinite strings | Theory of Computation | Kolmogorov complexity function | Computability | SCALED DIMENSION | MATHEMATICS | KOLMOGOROV COMPLEXITY | SEQUENCES | SETS | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Lower bounds | Upper bounds | Strings | Martingales | Complexity | Information theory

Hausdorff dimension | Super-martingales | Computer Science | Infinite strings | Theory of Computation | Kolmogorov complexity function | Computability | SCALED DIMENSION | MATHEMATICS | KOLMOGOROV COMPLEXITY | SEQUENCES | SETS | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Lower bounds | Upper bounds | Strings | Martingales | Complexity | Information theory

Journal Article

Inventiones Mathematicae, ISSN 0020-9910, 2009, Volume 178, Issue 3, pp. 635 - 654

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d...

ORIENTED PERCOLATION | BROWNIAN-MOTION | MATHEMATICS | PHASE | EXPONENTS | INEQUALITIES | SIMPLE RANDOM-WALK | CRITICAL-BEHAVIOR | INCIPIENT INFINITE CLUSTER | MEAN-FIELD CRITICALITY | QUENCHED INVARIANCE-PRINCIPLES | Studies

ORIENTED PERCOLATION | BROWNIAN-MOTION | MATHEMATICS | PHASE | EXPONENTS | INEQUALITIES | SIMPLE RANDOM-WALK | CRITICAL-BEHAVIOR | INCIPIENT INFINITE CLUSTER | MEAN-FIELD CRITICALITY | QUENCHED INVARIANCE-PRINCIPLES | Studies

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 05/2017, Volume 50, Issue 23, p. 235001

... their upper critical dimensions d(c). Behaviour at the critical point is non-universal in d > d(c) = 6 dimensions...

universality | finite-size scaling | percolation | critical phenomena | hyperscaling | upper critical dimension | clusters | INFINITE CLUSTERS | NUMBER | LACE EXPANSION | PHYSICS, MULTIDISCIPLINARY | PHASE-TRANSITIONS | INCIPIENT SPANNING CLUSTERS | PHYSICS, MATHEMATICAL | CRITICAL RANDOM GRAPHS | UNIQUENESS | PROBABILITY | CRITICAL-BEHAVIOR | RANDOM SUBGRAPHS | Physics - Statistical Mechanics

universality | finite-size scaling | percolation | critical phenomena | hyperscaling | upper critical dimension | clusters | INFINITE CLUSTERS | NUMBER | LACE EXPANSION | PHYSICS, MULTIDISCIPLINARY | PHASE-TRANSITIONS | INCIPIENT SPANNING CLUSTERS | PHYSICS, MATHEMATICAL | CRITICAL RANDOM GRAPHS | UNIQUENESS | PROBABILITY | CRITICAL-BEHAVIOR | RANDOM SUBGRAPHS | Physics - Statistical Mechanics

Journal Article

Physical review letters, ISSN 1079-7114, 2011, Volume 107, Issue 25, p. 256402

...) for the half-filled Hubbard model in three dimensions. The most relevant changes due to nonlocal fluctuations...

FERROMAGNETISM | SYSTEMS | PHYSICS, MULTIDISCIPLINARY | MEAN-FIELD THEORY | INFINITE DIMENSIONS | TRANSITION METALS | Physics - Strongly Correlated Electrons

FERROMAGNETISM | SYSTEMS | PHYSICS, MULTIDISCIPLINARY | MEAN-FIELD THEORY | INFINITE DIMENSIONS | TRANSITION METALS | Physics - Strongly Correlated Electrons

Journal Article

Journal of Complexity, ISSN 0885-064X, 04/2016, Volume 33, pp. 55 - 88

...-dimension of their unit balls. Here, the approximation is based on linear information. Such function spaces appear for example for the solution of parametric and stochastic PDEs...

[formula omitted]-dimension | Parametric and stochastic elliptic PDEs | Infinite-dimensional hyperbolic cross approximation | Mixed Sobolev–Korobov-type smoothness | Mixed Sobolev-analytic-type smoothness | Linear information | ε-dimension | Mixed Sobolev-Korobov-type smoothness | FUNCTION-SPACES | MATHEMATICS, APPLIED | NUMBER | TRACTABILITY | MONTE CARLO ALGORITHMS | LATTICE POINTS | MATHEMATICS | MULTILEVEL ALGORITHMS | STOCHASTIC COLLOCATION METHOD | INTEGRATION | PARTIAL-DIFFERENTIAL-EQUATIONS | epsilon-dimension | CONVERGENCE | Lower bounds | Approximation | Function space | Mathematical analysis | Constants | Stochasticity | Estimates | Smoothness

[formula omitted]-dimension | Parametric and stochastic elliptic PDEs | Infinite-dimensional hyperbolic cross approximation | Mixed Sobolev–Korobov-type smoothness | Mixed Sobolev-analytic-type smoothness | Linear information | ε-dimension | Mixed Sobolev-Korobov-type smoothness | FUNCTION-SPACES | MATHEMATICS, APPLIED | NUMBER | TRACTABILITY | MONTE CARLO ALGORITHMS | LATTICE POINTS | MATHEMATICS | MULTILEVEL ALGORITHMS | STOCHASTIC COLLOCATION METHOD | INTEGRATION | PARTIAL-DIFFERENTIAL-EQUATIONS | epsilon-dimension | CONVERGENCE | Lower bounds | Approximation | Function space | Mathematical analysis | Constants | Stochasticity | Estimates | Smoothness

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 06/2016, Volume 451, pp. 237 - 250

... themselves under the sole action of the Coulomb repulsion in many dimensions in the usual Euclidean space, therefore generalizing the so called Thomson problem to many dimensions...

Infinite charge system | Non-Euclidean geometries | Structures and symmetry in higher Euclidean dimensions | Thomson model | CRYSTAL | PHYSICS, MULTIDISCIPLINARY | Euclidean geometry | Sole | Confinement | Coulomb friction | Charge | Boundaries | Statistical mechanics | Optimization

Infinite charge system | Non-Euclidean geometries | Structures and symmetry in higher Euclidean dimensions | Thomson model | CRYSTAL | PHYSICS, MULTIDISCIPLINARY | Euclidean geometry | Sole | Confinement | Coulomb friction | Charge | Boundaries | Statistical mechanics | Optimization

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2017, Volume 50, Issue 15

We consider super-diffusive Levy walks in d >= 2 dimensions when the duration of a single step, i.e...

large deviations | random walk | central limit theorem | Lévy walks | fractional diffusion equation | fractional Laplacian | infinite density | PHYSICS, MULTIDISCIPLINARY | STATISTICS | TIME | PHYSICS, MATHEMATICAL | ANOMALOUS DIFFUSION | TRANSPORT | DENSITIES | Levy walks

large deviations | random walk | central limit theorem | Lévy walks | fractional diffusion equation | fractional Laplacian | infinite density | PHYSICS, MULTIDISCIPLINARY | STATISTICS | TIME | PHYSICS, MATHEMATICAL | ANOMALOUS DIFFUSION | TRANSPORT | DENSITIES | Levy walks

Journal Article