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• W1592218264 abstract "By defining tracial states on a non-commutative analogue of a path space, we construct Markov dilations for a class of conservative completely Markov semigroups on finite von Neumann algebras. This class includes all symmetric semigroups. For well chosen semigroups (for instance with generator any divergence form operator associated to a derivation valued in the coarse correspondence) those dilations give rise to stationary solutions of certain free SDEs previously considered by D. Shlyakhtenko. Among applications, we prove a non-commutative Talagrand inequality for non-microstates free entropy (relative to a subalgebra B and a completely positive map eta:Bto B). We also use those new deformations in conjunction with Popa's deformation/rigidity techniques. For instance, combining our results with techniques of Popa-Ozawa and Peterson, we prove that the von Neumann algebra of a countable discrete group with CMAP and positive first L^2 Betti number has no Cartan subalgebras." @default.
• W1592218264 created "2016-06-24" @default.
• W1592218264 creator A5052788604 @default.
• W1592218264 date "2010-06-22" @default.
• W1592218264 modified "2023-09-27" @default.
• W1592218264 title "A non-commutative Path Space approach to stationary free Stochastic Differential Equations" @default.
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• W1592218264 hasPublicationYear "2010" @default.
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