Electronic Journal of Probability

Random perturbations of hyperbolic dynamics

Florian Dorsch and Hermann Schulz-Baldes

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A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random perturbations it is shown that the dynamics approaches the stable fixed points of the unperturbed matrix up to errors even if the strength of the perturbation is large compared to the relative increase of nearby diagonal entries of the unperturbed matrix specifying the local hyperbolicity.

Article information

Electron. J. Probab., Volume 24 (2019), paper no. 89, 23 pp.

Received: 5 November 2018
Accepted: 7 July 2019
First available in Project Euclid: 10 September 2019

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Zentralblatt MATH identifier

Primary: 37H10: Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15] 37H15: Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx] 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Furstenberg measure random matrices random dynamical systems

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Dorsch, Florian; Schulz-Baldes, Hermann. Random perturbations of hyperbolic dynamics. Electron. J. Probab. 24 (2019), paper no. 89, 23 pp. doi:10.1214/19-EJP340. https://projecteuclid.org/euclid.ejp/1568080869

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