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Article Dans Une Revue Memoirs of the American Mathematical Society Année : 2023

THE REGULARITY OF THE LINEAR DRIFT IN NEGATIVELY CURVED SPACES

Lin Shu
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Résumé

We show the linear drift of the Brownian motion on the universal cover of a closed connected Riemannian manifold is C k´2 differentiable along any C k curve in the manifold of C k metrics with negative sectional curvature. We also show that the stochastic entropy of the Brownian motion is C 1 differentiable along any C 3 curve of C 3 metrics with negative sectional curvature. We formulate the first derivatives of the linear drift and entropy, respectively, and show they are critical at locally symmetric metrics.
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Dates et versions

hal-01630521 , version 1 (07-11-2017)
hal-01630521 , version 2 (11-05-2018)

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François Ledrappier, Lin Shu. THE REGULARITY OF THE LINEAR DRIFT IN NEGATIVELY CURVED SPACES. Memoirs of the American Mathematical Society, 2023, 281 (1387), ⟨10.1090/memo/1387⟩. ⟨hal-01630521v2⟩
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