Attracting edge property for a class of reinforced random walks

Annals of Probability

Volumn 31, Issue 3, 2003, Pages 1615-1654

  Limic, Vlada ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Coupling; Reinforced walk; Supermartingale; Urn

Indexed keywords

EID: 0038034721     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1055425792     Document Type: Article

References (15)

1. ATHREYA, K. B. and KARLIN, S. (1986). Embedding of Urn schemes into continuous time Markov branching processes and related limit theorems. Ann. Math. Statist. 39 1801-1817.
2. DAVIS, B. (1990). Reinforced random walk. Probab. Theory Random Fields 84 203-229.
3. DIACONIS, P. (1988). Recent progress on de Finetti's notion of exchangeability. In Bayesian Statistics 3 (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 43-110. Oxford Univ. Press.
4. DURRETT, R. (1991). Probability: Theory and Examples. Wadsworth and Brooks/Cole, Belmont, CA.
5. DURRETT, R., KESTEN, H. and LIMIC, V. (2002). Once edge-reinforced random walk on a tree. Probab. Theory Related Fields 122 567-592.
6. HILL, B. M., LANE, D. and SUDDERTH, W. A. (1980). Strong law for some generalized urn processes. Ann. Probab. 8 214-226.
7. KEANE, M. S. and ROLLES, S. W. W. (2000). Edge-reinforced random walk on finite graphs. In Infinite Dimensional Stochastic Analysis (P. Clement, F. den Hollander, J. van Neerven and B. de Pagter, eds.) 217-234. Royal Netherlands Academy of Arts and Sciences, Amsterdam.
8. PEMANTLE, R. (1988). Phase transition in reinforced random walk and RWRE on trees. Ann. Probab. 16 1229-1241.
9. PEMANTLE, R. (1992). Vertex-reinforced random walk. Probab. Theory Related Fields 92 117-136.
10. PEMANTLE, R. (2001). Random processes with reinforcement. Preprint.
11. PEMANTLE, R. and VOLKOV, S. (1999). Vertex-reinforced random walk on Z has finite range. Ann. Probab. 27 1368-1388.
12. SELLKE, T. (1994). Reinforced random walks on the d-dimensional integer lattice. Preprint.
13. TARRÈS, P. (2001). VRRW on Z eventually gets stuck at a set of five points. Preprint.
14. TÓTH, B. (1997). Limit theorems for weakly reinforced random walks on Z. Studia Sci. Math. Hungar. 33 321-337.
15. VOLKOV, S. (2001). Vertex-reinforced random walk on arbitrary graphs. Ann. Probab. 29 66-91.