Markov chain intersections and loop-erased walk

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 39, Issue 5, 2003, Pages 779-791

  Lyons, Russell ^a,b   Peres, Yuval ^c   Schramm, Oded ^d  

^a INDIANA UNIVERSITY   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d MICROSOFT RESEARCH   (United States)

Author keywords

Random walk; Uniform spanning forests

Indexed keywords

EID: 0042843663     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(03)00033-5     Document Type: Article

References (15)

1. Benjamini I. Lyons R. Peres Y. Schramm O. Uniform spanning forests Ann. Probab. 29 2001 1-65
2. Burkholder D.L. Davis B.J. Gundy R.F. Integral inequalities for convex functions of operators on martingales in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley 1970/1971), Vol. II: Probability Theory 1972 223-240 University California Press Berkeley
3. Erdos P. Taylor S.J. Some intersection properties of random walk paths Acta Math. Acad. Sci. Hungar. 11 1960 231-248
4. Fitzsimmons P.J. Salisbury T. Capacity and energy for multiparameter Markov processes Ann. Inst. H. Poincaré Probab. Statist. 25 1989 325-350
5. Häggström O. Random-cluster measures and uniform spanning trees Stochastic Process. Appl. 59 1995 267-275
6. N. James, Ph.D. Thesis, University of California, Berkeley, 1996
7. James N. Peres Y. Cutpoints and exchangeable events for random walks Teor. Veroyatnost. i Primenen. 41 1996 854-868 Reproduced in Theory Probab. Appl. 41 1997 666-677
8. Kahane J.-P. Some Random Series of Functions Second Edition 1985 Cambridge University Press Cambridge
9. Lawler G. Intersections of Random Walks 1991 Birkhäuser Boston
10. Lawler G. Loop-erased walks intersect infinitely often in four dimensions Electron. Comm. Probab. 3 1998 35-42
11. Le Gall J.-F. Rosen J. The range of stable random walks Ann. Probab. 19 1991 650-705
12. Pemantle R. Choosing a spanning tree for the integer lattice uniformly Ann. Probab. 19 1991 1559-1574
13. Salisbury T. Energy, and intersections of Markov chains in: Aldous D. Pemantle R. (Eds.), Random Discrete Structures The IMA Volumes in Mathematics and its Applications 76 1996 1996 213-225 Springer-Verlag New York
14. Wilson D.B. Generating random spanning trees more quickly than the cover time Proceedings of the Twenty-eighth Annual ACM Symposium on the Theory of Computing (Philadelphia, PA, 1996) 1996 296-303 ACM New York
15. Woess W. Random Walks on Infinite Graphs and Groups Cambridge Tracts in Math. 138 2000 Cambridge University Press Cambridge