1979, Lecture notes in mathematics, ISBN 9780387097121, Volume 760., viii, 190

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Quantum de Finetti theorems and mean-field theory from quantum phase space representations

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 02/2016, Volume 49, Issue 13, p. 135302

We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase...

de Finetti theorem | BoseEinstein condensate | mean-field theory | GASES | PHYSICS, MULTIDISCIPLINARY | SYMMETRIC STATES | SYSTEMS | ATOMS | CLASSICAL LIMIT | PHYSICS, MATHEMATICAL | Bose-Einstein condensate | Theorems | Approximation | Mathematical analysis | Evolution | Mathematical models | Inverse | Density | Quantum theory

de Finetti theorem | BoseEinstein condensate | mean-field theory | GASES | PHYSICS, MULTIDISCIPLINARY | SYMMETRIC STATES | SYSTEMS | ATOMS | CLASSICAL LIMIT | PHYSICS, MATHEMATICAL | Bose-Einstein condensate | Theorems | Approximation | Mathematical analysis | Evolution | Mathematical models | Inverse | Density | Quantum theory

Journal Article

ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, ISSN 1980-0436, 2016, Volume 13, Issue 2, pp. 1165 - 1187

A consequence of de Finetti's representation theorem is that for every infinite sequence of exchangeable 0-1 random variables (X-k)(k >= 1), there exists a...

de Finetti's theorem | Exchangeable Variables | LAWS | LARGE NUMBERS | STATISTICS | SETS | EXCHANGEABLE RANDOM-VARIABLES | Wasserstein distance | Urn models | HOEFFDING DECOMPOSITIONS | STATISTICS & PROBABILITY

de Finetti's theorem | Exchangeable Variables | LAWS | LARGE NUMBERS | STATISTICS | SETS | EXCHANGEABLE RANDOM-VARIABLES | Wasserstein distance | Urn models | HOEFFDING DECOMPOSITIONS | STATISTICS & PROBABILITY

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 05/2012, Volume 163, Issue 5, pp. 530 - 546

We prove a computable version of the de Finetti theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes...

Mutation | The de Finetti theorem | Probabilistic programming languages | Exchangeability | Computable probability theory | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | SPACES | PROBABILITY-MEASURES | LOGIC | RANDOM-VARIABLES

Mutation | The de Finetti theorem | Probabilistic programming languages | Exchangeability | Computable probability theory | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | SPACES | PROBABILITY-MEASURES | LOGIC | RANDOM-VARIABLES

Journal Article

TEST, ISSN 1133-0686, 3/2015, Volume 24, Issue 1, pp. 136 - 165

In the framework of a random assignment process—which randomly assigns an index within a finite set of labels to the points of an arbitrary set—we study...

Statistics for Business/Economics/Mathematical Finance/Insurance | Statistical Theory and Methods | 60G09 | Statistics, general | Strong laws of large numbers | De Finetti theorem | Statistics | Random assignment processes | Exchangeability | REPRESENTATION | STATISTICS & PROBABILITY | Studies | Theorems | Test methods | Information management | Labels | Law | Random variables | Mathematical analysis

Statistics for Business/Economics/Mathematical Finance/Insurance | Statistical Theory and Methods | 60G09 | Statistics, general | Strong laws of large numbers | De Finetti theorem | Statistics | Random assignment processes | Exchangeability | REPRESENTATION | STATISTICS & PROBABILITY | Studies | Theorems | Test methods | Information management | Labels | Law | Random variables | Mathematical analysis

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2010, Volume 258, Issue 4, pp. 1073 - 1120

The extended de Finetti theorem characterizes exchangeable infinite sequences of random variables as conditionally i.i.d. and shows that the apparently weaker...

Noncommutative Kolmogorov zero–one law | Mean ergodic theorem | Noncommutative Bernoulli shifts | Noncommutative conditional independence | Noncommutative de Finetti theorem | Distributional symmetries | Spreadability | Exchangeability | Noncommutative Kolmogorov zero-one law | VONNEUMANN-ALGEBRAS | RANDOM-VARIABLES | MATHEMATICS | PROBABILITY | GENERALIZED BROWNIAN-MOTION | SYMMETRIC STATES | DEFINETTIS THEOREM | CUMULANTS | W-STAR-ALGEBRAS | INTERACTING FOCK SPACES | CENTRAL-LIMIT-THEOREM

Noncommutative Kolmogorov zero–one law | Mean ergodic theorem | Noncommutative Bernoulli shifts | Noncommutative conditional independence | Noncommutative de Finetti theorem | Distributional symmetries | Spreadability | Exchangeability | Noncommutative Kolmogorov zero-one law | VONNEUMANN-ALGEBRAS | RANDOM-VARIABLES | MATHEMATICS | PROBABILITY | GENERALIZED BROWNIAN-MOTION | SYMMETRIC STATES | DEFINETTIS THEOREM | CUMULANTS | W-STAR-ALGEBRAS | INTERACTING FOCK SPACES | CENTRAL-LIMIT-THEOREM

Journal Article

Synthese, ISSN 0039-7857, 10/2017, Volume 194, Issue 10, pp. 4055 - 4063

We prove that de Finetti coherence is preserved under taking products of coherent books on two sets of independent events. This establishes a desirable closure...

De Finetti Dutch Book theorem | Philosophy of Science | 60B05 | Epistemology | Product measure | 28A35 | Free product | Coherent probability assessment | Carathéodory extension theorem | 18B35 | Coherent book | De Finetti coherent bet | Dutch Book | 18A30 | Logic | Product book | 06E15 | Independent events | Stone duality | Measure on a boolean algebra | Independence | Metaphysics | Independent boolean subagebras | 28A60 | Primary: 60A05 | Philosophy of Language | Secondary: 03G05 | Philosophy | HISTORY & PHILOSOPHY OF SCIENCE | PROBABILITY | Caratheodory extension theorem | PHILOSOPHY | Computer science | Algebra | Gambling | Theorems | Theoretical mathematics | Probability | Set theory

De Finetti Dutch Book theorem | Philosophy of Science | 60B05 | Epistemology | Product measure | 28A35 | Free product | Coherent probability assessment | Carathéodory extension theorem | 18B35 | Coherent book | De Finetti coherent bet | Dutch Book | 18A30 | Logic | Product book | 06E15 | Independent events | Stone duality | Measure on a boolean algebra | Independence | Metaphysics | Independent boolean subagebras | 28A60 | Primary: 60A05 | Philosophy of Language | Secondary: 03G05 | Philosophy | HISTORY & PHILOSOPHY OF SCIENCE | PROBABILITY | Caratheodory extension theorem | PHILOSOPHY | Computer science | Algebra | Gambling | Theorems | Theoretical mathematics | Probability | Set theory

Journal Article

Proceedings of the forty-fifth annual ACM symposium on theory of computing, ISSN 0737-8017, 06/2013, pp. 861 - 870

Quantum de Finetti theorems are a useful tool in the study of correlations in quantum multipartite states. In this paper we prove two new quantum de Finetti...

quantum information theory | SDP hierarchy | de finetti | De finetti | Quantum information theory

quantum information theory | SDP hierarchy | de finetti | De finetti | Quantum information theory

Conference Proceeding

Fuzzy Sets and Systems, ISSN 0165-0114, 02/2016, Volume 284, pp. 1 - 30

We provide representation theorems for both finite and countable sequences of finite-valued random variables that are considered to be partially exchangeable....

Partial exchangeability | de Finetti's representation theorem | Indifferent gambles | Sets of desirable gambles | Lower previsions | DESIRABLE GAMBLES | FINITE ADDITIVITY | MATHEMATICS, APPLIED | SEQUENCES | STATISTICS & PROBABILITY | MULTINOMIAL DATA | MODEL | IMPRECISE PROBABILITY | SETS | COMPUTER SCIENCE, THEORY & METHODS

Partial exchangeability | de Finetti's representation theorem | Indifferent gambles | Sets of desirable gambles | Lower previsions | DESIRABLE GAMBLES | FINITE ADDITIVITY | MATHEMATICS, APPLIED | SEQUENCES | STATISTICS & PROBABILITY | MULTINOMIAL DATA | MODEL | IMPRECISE PROBABILITY | SETS | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 01/2016, Volume 441, pp. 23 - 31

The Boltzmann–Gibbs entropy is known to be asymptotically extensive for the Laplace–de Finetti distribution. We prove here that the same result holds in the...

Rényi | Binomial distribution | Entropy | Extensivity | Laplace–de Finetti representation | Laplace-de Finetti representation | Renyi | PHYSICS, MULTIDISCIPLINARY

Rényi | Binomial distribution | Entropy | Extensivity | Laplace–de Finetti representation | Laplace-de Finetti representation | Renyi | PHYSICS, MULTIDISCIPLINARY

Journal Article

Statistical Science, ISSN 0883-4237, 11/1993, Volume 8, Issue 4, pp. 433 - 457

The three main points of this article are: 1. Quantum mechanical data differ from conventional data: for example, joint distributions usually cannot be defined...

Statistical inferences | Uncertainty principle | Quantum mechanics | Quantum statistics | Eigenvalues | Hilbert spaces | Eigenvectors | Quantum field theory | Physics | Probabilities | Heisenberg uncertainty | Probability-operator measure | Self-adjoint operator | De finetti representation theorem | Spectral measure | Cramér-rao inequality | Decision theory | Hilbert space | Bayesian inference | Joint distribution | DECISION THEORY | DEFINETTI REPRESENTATION THEOREM | CRAMER-RAO INEQUALITY | INFORMATION | STATISTICS & PROBABILITY | COHERENT STATES | SELF-ADJOINT OPERATOR | QUANTUM MECHANICS | JOINT DISTRIBUTION | SPECTRAL MEASURE | PROBABILITY-OPERATOR MEASURE | BAYESIAN INFERENCE | HEISENBERG UNCERTAINTY | HILBERT SPACE | PHASE MEASUREMENT | COMMUNICATION | self-adjoint operator | probability-operator measure | decision theory | de Finetti representation theorem | Cramer-Rao inequality | joint distribution | spectral measure

Statistical inferences | Uncertainty principle | Quantum mechanics | Quantum statistics | Eigenvalues | Hilbert spaces | Eigenvectors | Quantum field theory | Physics | Probabilities | Heisenberg uncertainty | Probability-operator measure | Self-adjoint operator | De finetti representation theorem | Spectral measure | Cramér-rao inequality | Decision theory | Hilbert space | Bayesian inference | Joint distribution | DECISION THEORY | DEFINETTI REPRESENTATION THEOREM | CRAMER-RAO INEQUALITY | INFORMATION | STATISTICS & PROBABILITY | COHERENT STATES | SELF-ADJOINT OPERATOR | QUANTUM MECHANICS | JOINT DISTRIBUTION | SPECTRAL MEASURE | PROBABILITY-OPERATOR MEASURE | BAYESIAN INFERENCE | HEISENBERG UNCERTAINTY | HILBERT SPACE | PHASE MEASUREMENT | COMMUNICATION | self-adjoint operator | probability-operator measure | decision theory | de Finetti representation theorem | Cramer-Rao inequality | joint distribution | spectral measure

Journal Article

Soft Computing, ISSN 1432-7643, 4/2019, Volume 23, Issue 7, pp. 2289 - 2295

de Finetti’s Dutch book theorem explains why probability has to be additive on disjunctions of incompatible yes–no (Boolean) events. The theorem holds verbatim...

Dutch book | Product measure | Free product | Coherent probability assessment | Carathéodory extension theorem | Engineering | Computational Intelligence | Coherent book | de Finetti’s coherent bet | Random variable | Product book | Independent events | Stone duality | Artificial Intelligence | Independence | Gamma $$ Γ functor | Riesz representation theorem | MV-algebraic tensor | Łukasiewicz logic | Measure on a Boolean algebra | Control, Robotics, Mechatronics | Continuous event | Product law | de Finetti’s Dutch book theorem | Independent Boolean subalgebras | Mathematical Logic and Foundations | Γ functor | THEOREM | functor | Caratheodory extension theorem | de Finetti's coherent bet | COHERENCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ukasiewicz logic | de Finetti's Dutch book theorem | Computer science | Algebra

Dutch book | Product measure | Free product | Coherent probability assessment | Carathéodory extension theorem | Engineering | Computational Intelligence | Coherent book | de Finetti’s coherent bet | Random variable | Product book | Independent events | Stone duality | Artificial Intelligence | Independence | Gamma $$ Γ functor | Riesz representation theorem | MV-algebraic tensor | Łukasiewicz logic | Measure on a Boolean algebra | Control, Robotics, Mechatronics | Continuous event | Product law | de Finetti’s Dutch book theorem | Independent Boolean subalgebras | Mathematical Logic and Foundations | Γ functor | THEOREM | functor | Caratheodory extension theorem | de Finetti's coherent bet | COHERENCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ukasiewicz logic | de Finetti's Dutch book theorem | Computer science | Algebra

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 7/2014, Volume 104, Issue 7, pp. 871 - 891

We prove the existence of scattering states for the defocusing cubic Gross–Pitaevskii (GP) hierarchy in $${\mathbb{R}^3}$$ R 3 . Moreover, we show that an...

Theoretical, Mathematical and Computational Physics | ill-posedness | 35Q55 | Statistical Physics, Dynamical Systems and Complexity | blowup | nonlinear Schrödinger equation | Physics | Geometry | quantum de Finetti theorem | scattering | Gross–Pitaevskii hierarchy | Group Theory and Generalizations | 81V70 | Gross-Pitaevskii hierarchy | MEAN-FIELD-LIMIT | nonlinear Schrodinger equation | CLASSICAL-LIMIT | CAUCHY-PROBLEM | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | BOSE-EINSTEIN CONDENSATION | BOSONS | UNIQUENESS | RIGOROUS DERIVATION | DYNAMICS

Theoretical, Mathematical and Computational Physics | ill-posedness | 35Q55 | Statistical Physics, Dynamical Systems and Complexity | blowup | nonlinear Schrödinger equation | Physics | Geometry | quantum de Finetti theorem | scattering | Gross–Pitaevskii hierarchy | Group Theory and Generalizations | 81V70 | Gross-Pitaevskii hierarchy | MEAN-FIELD-LIMIT | nonlinear Schrodinger equation | CLASSICAL-LIMIT | CAUCHY-PROBLEM | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | BOSE-EINSTEIN CONDENSATION | BOSONS | UNIQUENESS | RIGOROUS DERIVATION | DYNAMICS

Journal Article

TEST, ISSN 1133-0686, 8/2011, Volume 20, Issue 2, pp. 293 - 310

We impose conditions on a family of 0–1 random variables ensuring that they verify a de Finetti-type theorem. More precisely, we assume that the 0–1 random...

Statistics for Business/Economics/Mathematical Finance/Insurance | Random selection processes | Statistical Theory and Methods | 60G09 | Statistics, general | De Finetti theorem | Statistics | Exchangeability | STATISTICS & PROBABILITY | Studies | Analysis | Random variables | Exchange

Statistics for Business/Economics/Mathematical Finance/Insurance | Random selection processes | Statistical Theory and Methods | 60G09 | Statistics, general | De Finetti theorem | Statistics | Exchangeability | STATISTICS & PROBABILITY | Studies | Analysis | Random variables | Exchange

Journal Article

Biometrical Journal, ISSN 0323-3847, 01/2018, Volume 60, Issue 1, pp. 146 - 154

In clinical research and in more general classification problems, a frequent concern is the reliability of a rating system. In the absence of a gold standard,...

agreement | correlated kappa statistics | inflammatory bowel diseases | de Finetti representation theorem | STATISTICS & PROBABILITY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Gastrointestinal diseases | Confidence intervals | Inflammatory bowel diseases | Endoscopes | Statistical analysis | Intestine | Asymptotic properties | Data processing | Endoscopy

agreement | correlated kappa statistics | inflammatory bowel diseases | de Finetti representation theorem | STATISTICS & PROBABILITY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Gastrointestinal diseases | Confidence intervals | Inflammatory bowel diseases | Endoscopes | Statistical analysis | Intestine | Asymptotic properties | Data processing | Endoscopy

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 2009, Volume 161, Issue 2, pp. 235 - 245

De Finetti gave a natural definition of “coherent probability assessment” β : E → [ 0 , 1 ] of a set E = { X 1 , … , X m } of “events” occurring in an...

De Finetti coherence criterion | Dutch book | Lukasiewicz logic | Borel probability measure | Many-valued logics | MV-algebra | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | THEOREM | LOGIC

De Finetti coherence criterion | Dutch book | Lukasiewicz logic | Borel probability measure | Many-valued logics | MV-algebra | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | THEOREM | LOGIC

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 05/2014, Volume 266, Issue 10, pp. 6055 - 6157

This paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by M. Kac [41] in his study of...

Qualitative chaos | CLT with optimal rate | Quantitative chaos | Mean-field limit | De Finetti, Hewitt and Savage theorem | Entropy chaos | Probability measures mixtures | Kac's chaos | Fisher information chaos | Monge–Kantorovich–Wasserstein distance | Monge-Kantorovich-Wasserstein distance | Monge Kantorovich Wasserstein distance | STATISTICAL-MECHANICS | STATIONARY FLOWS | FISHER INFORMATION | INEQUALITIES | APPROXIMATION | 2-DIMENSIONAL EULER EQUATIONS | MATHEMATICS | EQUILIBRIUM | PROPAGATION | CENTRAL-LIMIT-THEOREM | ENTROPY | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Qualitative chaos | CLT with optimal rate | Quantitative chaos | Mean-field limit | De Finetti, Hewitt and Savage theorem | Entropy chaos | Probability measures mixtures | Kac's chaos | Fisher information chaos | Monge–Kantorovich–Wasserstein distance | Monge-Kantorovich-Wasserstein distance | Monge Kantorovich Wasserstein distance | STATISTICAL-MECHANICS | STATIONARY FLOWS | FISHER INFORMATION | INEQUALITIES | APPROXIMATION | 2-DIMENSIONAL EULER EQUATIONS | MATHEMATICS | EQUILIBRIUM | PROPAGATION | CENTRAL-LIMIT-THEOREM | ENTROPY | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2017, Volume 369, Issue 1, pp. 645 - 679

We introduce symmetric states and quantum symmetric states on universal unital free product C^*-algebras of the form {\mathfrak{A}}=\operatornamewithlimits...

Amalgamated free product | De Finetti theorem | Quantum exchangeable | Quantum symmetric states | MATHEMATICS | de Finetti theorem | FINETTI THEOREM | amalgamated free product | quantum exchangeable

Amalgamated free product | De Finetti theorem | Quantum exchangeable | Quantum symmetric states | MATHEMATICS | de Finetti theorem | FINETTI THEOREM | amalgamated free product | quantum exchangeable

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 04/2005, Volume 18, Issue 2, pp. 399 - 412

For probability measures on product spaces which are symmetric under permutations of coordinates, we study the rate of approximation by mixtures of product...

Symmetric polynomials | induction | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | quadratic | de Finetti representation | Induction | Quadratic | De Finetti representation | quadratics induction | EXCHANGEABLE RANDOM-VARIABLES | STATISTICS & PROBABILITY | symmetric polynomials | CENTRAL-LIMIT-THEOREM

Symmetric polynomials | induction | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | quadratic | de Finetti representation | Induction | Quadratic | De Finetti representation | quadratics induction | EXCHANGEABLE RANDOM-VARIABLES | STATISTICS & PROBABILITY | symmetric polynomials | CENTRAL-LIMIT-THEOREM

Journal Article