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Excursions of excited random walks on integers


 
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1. Title Title of document Excursions of excited random walks on integers
 
2. Creator Author's name, affiliation, country Elena Kosygina; Baruch College and the CUNY Graduate Center; United States
 
2. Creator Author's name, affiliation, country Martin P. W. Zerner; University of Tuebingen; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) branching process, cookie walk, diffusion approximation, excited random walk, excursion, squared Bessel process, return time, strong transience
 
3. Subject Subject classification 60G50; 60K37; 60F17; 60J70; 60J80; 60J85
 
4. Description Abstract Several phase transitions for excited random walks on the integers are known to be characterized by a certain drift parameter $\delta\in\mathbb R$. For recurrence/transience the critical threshold is $|\delta|=1$, for ballisticity it is $|\delta|=2$ and for diffusivity $|\delta|=4$. In this paper we establish a phase transition at $|\delta|=3$. We show that the  expected return time of the walker to the starting point, conditioned on return, is finite iff $|\delta|>3$.  This result follows from an explicit description of the tail behaviour of the return time as a function of $\delta$, which is achieved by diffusion approximation of related branching processes by squared Bessel processes.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Simons Foundation, European Research Council
 
7. Date (YYYY-MM-DD) 2014-02-28
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2940
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2940
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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