The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Vladimir V. V'yugin - One of the best experts on this subject based on the ideXlab platform.
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On Stability Property of Probability Laws with Respect to Small Violations of Algorithmic Randomness
arXiv: Computational Complexity, 2014Co-Authors: Vladimir V. V'yuginAbstract:We study a stability property of probability laws with respect to small violations of algorithmic randomness. A sufficient condition of stability is presented in terms of Schnorr tests of algorithmic randomness. Most probability laws, like the strong law of large numbers, the law of iterated logarithm, and even Birkhoff's pointwise Ergodic theorem for Ergodic transformations, are stable in this sense. Nevertheless, the phenomenon of instability occurs in Ergodic theory. Firstly, the stability property of the Birkhoff's Ergodic theorem is non-uniform. Moreover, a computable non-Ergodic Measure preserving transformation can be constructed such that Ergodic theorem is non-stable. We also show that any universal data compression scheme is also non-stable with respect to the class of all computable Ergodic Measures.
Sorin Popa - One of the best experts on this subject based on the ideXlab platform.
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on a class of ii1 factors with at most one cartan subalgebra
Annals of Mathematics, 2010Co-Authors: Narutaka Ozawa, Sorin PopaAbstract:We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(F-r) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q (circle times) over barL(F-r), with Q an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free Ergodic Measure-preserving action of a free group F-r, 2 <= r <= infinity, on a probability space (X, mu) is profinite then the group Measure space factor L-infinity (X) F-r has unique Cartan subalgebra, up to unitary conjugacy.
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On a class of II1 factors with at most one Cartan subalgebra
Annals of Mathematics, 2010Co-Authors: Narutaka Ozawa, Sorin PopaAbstract:We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(F-r) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q (circle times) over barL(F-r), with Q an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free Ergodic Measure-preserving action of a free group F-r, 2
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actions of _ whose ii factors and orbit equivalence relations have prescribed fundamental group
Journal of the American Mathematical Society, 2009Co-Authors: Sorin Popa, Stefaan VaesAbstract:We show that given any subgroup F of R+ which is either countable or belongs to a certain “large” class of uncountable subgroups, there exist continuously many free Ergodic Measure preserving actions i of the free group with infinitely many generators F1 on probability Measure spaces (Xi,µi) such that their associated group Measure space II1 factors Mi = L 1 (Xi)o i F1 and orbit equivalence relationsRi =R(F1 y Xi) have fundamental group equal toF and with Mi (respectivelyRi) stably non-isomorphic. Moreover, these actions can be taken so thatRi has no outer automorphisms and any automorphism of Mi is unitary conjugate to an automorphism that acts trivially on the subalgebra L 1 (Xi) of Mi.
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Actions of _{∞} whose II₁ factors and orbit equivalence relations have prescribed fundamental group
Journal of the American Mathematical Society, 2009Co-Authors: Sorin Popa, Stefaan VaesAbstract:We show that given any subgroup F of R+ which is either countable or belongs to a certain “large” class of uncountable subgroups, there exist continuously many free Ergodic Measure preserving actions i of the free group with infinitely many generators F1 on probability Measure spaces (Xi,µi) such that their associated group Measure space II1 factors Mi = L 1 (Xi)o i F1 and orbit equivalence relationsRi =R(F1 y Xi) have fundamental group equal toF and with Mi (respectivelyRi) stably non-isomorphic. Moreover, these actions can be taken so thatRi has no outer automorphisms and any automorphism of Mi is unitary conjugate to an automorphism that acts trivially on the subalgebra L 1 (Xi) of Mi.
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on a class of mathrm ii _1 factors with at most one cartan subalgebra
arXiv: Operator Algebras, 2007Co-Authors: Narutaka Ozawa, Sorin PopaAbstract:We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra. Moreover, any II$_1$ factor of the form $Q \vt L(\Bbb F_r) $, with $Q$ an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free Ergodic Measure preserving action of a free group $\Bbb F_r$, $2\leq r \leq \infty$, on a probability space $(X,\mu)$ is profinite then the group Measure space factor $L^\infty(X)\rtimes \Bbb F_r$ has unique Cartan subalgebra, up to unitary conjugacy.
Maryam Mirzakhani - One of the best experts on this subject based on the ideXlab platform.
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Invariant and stationary Measures for the action on Moduli space
Publications mathématiques de l'IHÉS, 2018Co-Authors: Alex Eskin, Maryam MirzakhaniAbstract:We prove some Ergodic-theoretic rigidity properties of the action of on moduli space. In particular, we show that any Ergodic Measure invariant under the action of the upper triangular subgroup of is supported on an invariant affine submanifold. The main theorems are inspired by the results of several authors on unipotent flows on homogeneous spaces, and in particular by Ratner’s seminal work.
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invariant and stationary Measures for the sl 2 r action on moduli space
arXiv: Dynamical Systems, 2013Co-Authors: Alex Eskin, Maryam MirzakhaniAbstract:We prove some Ergodic-theoretic rigidity properties of the action of SL(2,R) on moduli space. In particular, we show that any Ergodic Measure invariant under the action of the upper triangular subgroup of SL(2,R) is supported on an invariant affine submanifold. The main theorems are inspired by the results of several authors on unipotent flows on homogeneous spaces, and in particular by Ratner's seminal work.
Narutaka Ozawa - One of the best experts on this subject based on the ideXlab platform.
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on a class of ii1 factors with at most one cartan subalgebra
Annals of Mathematics, 2010Co-Authors: Narutaka Ozawa, Sorin PopaAbstract:We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(F-r) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q (circle times) over barL(F-r), with Q an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free Ergodic Measure-preserving action of a free group F-r, 2 <= r <= infinity, on a probability space (X, mu) is profinite then the group Measure space factor L-infinity (X) F-r has unique Cartan subalgebra, up to unitary conjugacy.
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On a class of II1 factors with at most one Cartan subalgebra
Annals of Mathematics, 2010Co-Authors: Narutaka Ozawa, Sorin PopaAbstract:We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(F-r) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q (circle times) over barL(F-r), with Q an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free Ergodic Measure-preserving action of a free group F-r, 2
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on a class of mathrm ii _1 factors with at most one cartan subalgebra
arXiv: Operator Algebras, 2007Co-Authors: Narutaka Ozawa, Sorin PopaAbstract:We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra. Moreover, any II$_1$ factor of the form $Q \vt L(\Bbb F_r) $, with $Q$ an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free Ergodic Measure preserving action of a free group $\Bbb F_r$, $2\leq r \leq \infty$, on a probability space $(X,\mu)$ is profinite then the group Measure space factor $L^\infty(X)\rtimes \Bbb F_r$ has unique Cartan subalgebra, up to unitary conjugacy.
O N Ageev - One of the best experts on this subject based on the ideXlab platform.
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the homogeneous spectrum problem in Ergodic theory
Inventiones Mathematicae, 2005Co-Authors: O N AgeevAbstract:We prove that for any n≥2 there exists an Ergodic Measure-preserving transformation with homogeneous spectrum of multiplicity n in the orthogonal complement of the constant functions. This gives a complete solution of Rokhlin’s problem on homogeneous spectrum in Ergodic theory. The transformations we provide belong to the class of finite rank transformations.