Electronic Journal of Probability
- Electron. J. Probab.
- Volume 21 (2016), paper no. 70, 24 pp.
Functional limit laws for recurrent excited random walks with periodic cookie stacks
We consider one-dimensional excited random walks (ERWs) with periodic cookie stacks in the recurrent regime. We prove functional limit theorems for these walks which extend the previous results in [DK12] for excited random walks with “boundedly many cookies per site.” In particular, in the non-boundary recurrent case the rescaled excited random walk converges in the standard Skorokhod topology to a Brownian motion perturbed at its extrema (BMPE). While BMPE is a natural limiting object for excited random walks with boundedly many cookies per site, it is far from obvious why the same should be true for our model which allows for infinitely many “cookies” at each site. Moreover, a BMPE has two parameters $\alpha ,\beta <1$ and the scaling limits in this paper cover a larger variety of choices for $\alpha $ and $\beta $ than can be obtained for ERWs with boundedly many cookies per site.
Electron. J. Probab., Volume 21 (2016), paper no. 70, 24 pp.
Received: 12 April 2016
Accepted: 11 November 2016
First available in Project Euclid: 2 December 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F17: Functional limit theorems; invariance principles 60J15
Kosygina, Elena; Peterson, Jonathon. Functional limit laws for recurrent excited random walks with periodic cookie stacks. Electron. J. Probab. 21 (2016), paper no. 70, 24 pp. doi:10.1214/16-EJP14. https://projecteuclid.org/euclid.ejp/1480688087