Electronic Journal of Probability

Random walks veering left

Raoul Normand and Bálint Virág

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064314

Digital Object Identifier
doi:10.1214/EJP.v18-2523

Mathematical Reviews number (MathSciNet)
MR3126572

Zentralblatt MATH identifier
1296.60117

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

Keywords
Random walk Hausdorff dimension coupling random matrix Gaussian analytic function

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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