The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Wouter Vergote - One of the best experts on this subject based on the ideXlab platform.
-
Von Neumann-Morgenstern farsightedly stable setsin two-sided matching
2008Co-Authors: Ana Mauleon, Vincent Vannetelbosch, Wouter VergoteAbstract:We adopt the notion of Von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of Von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a Von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the Von Neumann-Morgenstern (myopically) stable sets, Von Neumann-Morgenstern farsightedly stable sets cannot include matchings that are not corewise stable ones. Moreover, we show that our main result is robust to many-to-one matching problems with responsive preferences.
-
Von Neumann-Morgenstern Farsightedly Stable Sets in Two-sided Matching
SSRN Electronic Journal, 2008Co-Authors: Ana Mauleon, Vincent Vannetelbosch, Wouter VergoteAbstract:We adopt the notion of Von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of Von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a Von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the Von Neumann-Morgenstern (myopically) stable sets, Von Neumann-Morgenstern farsightedly stable sets cannot include matchings that are not corewise stable ones. Moreover, we show that our main result is robust to many- to-one matching problems with responsive preferences.
Roberto Longo - One of the best experts on this subject based on the ideXlab platform.
-
Von Neumann Entropy in QFT.
Communications in Mathematical Physics, 2020Co-Authors: Roberto LongoAbstract:In the framework of Quantum Field Theory, we provide a rigorous, operator algebraic notion of entanglement entropy associated with a pair of open double cones $O \subset \tilde O$ of the spacetime, where the closure of $O$ is contained in $\tilde O$. Given a QFT net $A$ of local Von Neumann algebras $A(O)$, we consider the Von Neumann entropy $S_A(O, \tilde O)$ of the restriction of the vacuum state to the canonical intermediate type $I$ factor for the inclusion of Von Neumann algebras $A(O)\subset A(\tilde O)$ (split property). We show that this canonical entanglement entropy $S_A(O, \tilde O)$ is finite for the chiral conformal net on the circle generated by finitely many free Fermions (here double cones are intervals). To this end, we first study the notion of Von Neumann entropy of a closed real linear subspace of a complex Hilbert space, that we then estimate for the local free fermion subspaces. We further consider the lower entanglement entropy $\underline S_A(O, \tilde O)$, the infimum of the vacuum Von Neumann entropy of $F$, where $F$ here runs over all the intermediate, discrete type $I$ Von Neumann algebras. We prove that $\underline S_A(O, \tilde O)$ is finite for the local chiral conformal net generated by finitely many commuting $U(1)$-currents.
-
Von Neumann Entropy in QFT
Communications in Mathematical Physics, 2020Co-Authors: Roberto Longo, Feng XuAbstract:In the framework of Quantum Field Theory, we provide a rigorous, operator algebraic notion of entanglement entropy associated with a pair of open double cones $$O \subset {\widetilde{O}}$$ O ⊂ O ~ of the spacetime, where the closure of O is contained in $${\widetilde{O}}$$ O ~ . Given a QFT net $${\mathcal {A}}$$ A of local Von Neumann algebras $${\mathcal {A}}(O)$$ A ( O ) , we consider the Von Neumann entropy $$S_{\mathcal {A}}(O, {\widetilde{O}})$$ S A ( O , O ~ ) of the restriction of the vacuum state to the canonical intermediate type I factor for the inclusion of Von Neumann algebras $${\mathcal {A}}(O)\subset {\mathcal {A}}({\widetilde{O}})$$ A ( O ) ⊂ A ( O ~ ) (split property). We show that this canonical entanglement entropy $$S_{\mathcal {A}}(O, {\widetilde{O}})$$ S A ( O , O ~ ) is finite for the chiral conformal net on the circle generated by finitely many free Fermions (here double cones are intervals). To this end, we first study the notion of Von Neumann entropy of a closed real linear subspace of a complex Hilbert space, that we then estimate for the local free fermion subspaces. We further consider the lower entanglement entropy $${\underline{S}}_{\mathcal {A}}(O, {\widetilde{O}})$$ S ̲ A ( O , O ~ ) , the infimum of the vacuum Von Neumann entropy of $${\mathcal {F}}$$ F , where $${\mathcal {F}}$$ F here runs over all the intermediate, discrete type I Von Neumann algebras. We prove that $${\underline{S}}_{\mathcal {A}}(O, {\widetilde{O}})$$ S ̲ A ( O , O ~ ) is finite for the local chiral conformal net generated by finitely many commuting U (1)-currents.
-
Homomorphisms of Von Neumann Algebras
Tensor Categories and Endomorphisms of von Neumann Algebras, 2015Co-Authors: Marcel Bischoff, Roberto Longo, Yasuyuki Kawahigashi, Karl-henning RehrenAbstract:We introduce the tensor category structure of endomorphisms of infinite (type III) Von Neumann factors. We review the basic concepts of conjugate homomorphisms between a pair of infinite factors, including the dimension, and discuss the generalization to homomorphisms of a factor into a Von Neumann algebra with a centre.
Ana Mauleon - One of the best experts on this subject based on the ideXlab platform.
-
Von Neumann-Morgenstern farsightedly stable setsin two-sided matching
2008Co-Authors: Ana Mauleon, Vincent Vannetelbosch, Wouter VergoteAbstract:We adopt the notion of Von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of Von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a Von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the Von Neumann-Morgenstern (myopically) stable sets, Von Neumann-Morgenstern farsightedly stable sets cannot include matchings that are not corewise stable ones. Moreover, we show that our main result is robust to many-to-one matching problems with responsive preferences.
-
Von Neumann-Morgenstern Farsightedly Stable Sets in Two-sided Matching
SSRN Electronic Journal, 2008Co-Authors: Ana Mauleon, Vincent Vannetelbosch, Wouter VergoteAbstract:We adopt the notion of Von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of Von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a Von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the Von Neumann-Morgenstern (myopically) stable sets, Von Neumann-Morgenstern farsightedly stable sets cannot include matchings that are not corewise stable ones. Moreover, we show that our main result is robust to many- to-one matching problems with responsive preferences.
László Zsidó - One of the best experts on this subject based on the ideXlab platform.
-
The Commutation Theorem for Tensor Products over Von Neumann Algebras
Journal of Functional Analysis, 1999Co-Authors: Şerban Strătilă, László ZsidóAbstract:Abstract A general commutation theorem is proved for tensor products of Von Neumann algebras over common Von Neumann subalgebras. Roughly speaking, if the non-common parts of two Von Neumann algebras M 1 and M 2 on the same Hilbert space are appropriately separated by commuting type I Von Neumann algebras N 1 and N 2 , then the commutant of the Von Neumann algebra generated by M 1 and M 2 is generated by the relative commutants M ′ 1 ∩ N 1 and M ′ 2 ∩ N 2 , as well as by the intersection of the commutants of all concerned Von Neumann algebras. This theorem extends both Tomita's classical commutation theorem and a splitting result in tensor products, proved recently in the factor case by L. Ge and R. V. Kadison. Applications are given to a decomposition criterion in ordinary tensor products and to a partial solution of a conjecture of S. Popa concerning the maximal injectivity of tensor products of maximal injective Von Neumann subalgebras.
Vincent Vannetelbosch - One of the best experts on this subject based on the ideXlab platform.
-
Von Neumann-Morgenstern farsightedly stable setsin two-sided matching
2008Co-Authors: Ana Mauleon, Vincent Vannetelbosch, Wouter VergoteAbstract:We adopt the notion of Von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of Von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a Von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the Von Neumann-Morgenstern (myopically) stable sets, Von Neumann-Morgenstern farsightedly stable sets cannot include matchings that are not corewise stable ones. Moreover, we show that our main result is robust to many-to-one matching problems with responsive preferences.
-
Von Neumann-Morgenstern Farsightedly Stable Sets in Two-sided Matching
SSRN Electronic Journal, 2008Co-Authors: Ana Mauleon, Vincent Vannetelbosch, Wouter VergoteAbstract:We adopt the notion of Von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of Von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a Von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the Von Neumann-Morgenstern (myopically) stable sets, Von Neumann-Morgenstern farsightedly stable sets cannot include matchings that are not corewise stable ones. Moreover, we show that our main result is robust to many- to-one matching problems with responsive preferences.