Electronic Journal of Probability

Random walks veering left

Raoul Normand and Bálint Virág

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We study coupled random walks in the plane such that, at each step, the walks change direction by a uniform random angle plus an extra deterministic angle $\theta$. We compute the Hausdorff dimension of the $\theta$ for which the walk has an unusual behavior. This model is related to a study of the spectral measure of some random matrices. The same techniques allow to study the boundary behavior of some Gaussian analytic functions.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 89, 25 pp.

Accepted: 21 October 2013
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Random walk Hausdorff dimension coupling random matrix Gaussian analytic function

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Normand, Raoul; Virág, Bálint. Random walks veering left. Electron. J. Probab. 18 (2013), paper no. 89, 25 pp. doi:10.1214/EJP.v18-2523. https://projecteuclid.org/euclid.ejp/1465064314

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