1. Scaling limits of recurrent excited random walks on integers
- Author
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Elena Kosygina and Dmitry Dolgopyat
- Subjects
Statistics and Probability ,60G50 ,random environment ,60K37, 60F17, 60G50 ,Boundary (topology) ,01 natural sciences ,Measure (mathematics) ,Combinatorics ,010104 statistics & probability ,symbols.namesake ,Wiener process ,perturbed Brownian motion ,cookie walk ,FOS: Mathematics ,0101 mathematics ,Scaling ,Brownian motion ,Mathematics ,Branching process ,Discrete mathematics ,Probability (math.PR) ,010102 general mathematics ,Random walk ,branching process ,excited random walk ,60K37 ,60F17 ,Bounded function ,symbols ,Statistics, Probability and Uncertainty ,Mathematics - Probability - Abstract
We describe scaling limits of recurrent excited random walks (ERWs) on integers in i.i.d. cookie environments with a bounded number of cookies per site. We allow both positive and negative excitations. It is known that ERW is recurrent if and only if the expected total drift per site, delta, belongs to the interval [-1,1]. We show that if |delta, 12 pages
- Published
- 2012