Markov chain intersections and the loop-erased walk

 Access to full text

 Full (PDF)

1. [1] I. Benjamini, R. Lyons, Y. Peres, O. Schramm, Uniform spanning forests, Ann. Probab.29 (2001) 1-65. Zbl1016.60009MR1825141
2. [2] D.L. Burkholder, B.J. Davis, R.F. Gundy, 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, University California Press, Berkeley, 1972, pp. 223-240. Zbl0253.60056MR400380
3. [3] P. Erdős, S.J. Taylor, Some intersection properties of random walk paths, Acta Math. Acad. Sci. Hungar.11 (1960) 231-248. Zbl0096.33302MR126299
4. [4] P.J. Fitzsimmons, T. Salisbury, Capacity and energy for multiparameter Markov processes, Ann. Inst. H. Poincaré Probab. Statist.25 (1989) 325-350. Zbl0689.60071MR1023955
5. [5] O. Häggström, Random-cluster measures and uniform spanning trees, Stochastic Process. Appl.59 (1995) 267-275. Zbl0840.60089MR1357655
6. [6] N. James, Ph.D. Thesis, University of California, Berkeley, 1996. 
7. [7] N. James, Y. Peres, Cutpoints and exchangeable events for random walks, Teor. Veroyatnost. i Primenen.41 (1996) 854-868, Reproduced in , Theory Probab. Appl.41 (1997) 666-677. Zbl0896.60035MR1687097
8. [8] J.-P. Kahane, Some Random Series of Functions, Cambridge University Press, Cambridge, 1985. Zbl0571.60002MR833073
9. [9] G. Lawler, Intersections of Random Walks, Birkhäuser, Boston, 1991. Zbl0925.60078MR1117680
10. [10] G. Lawler, Loop-erased walks intersect infinitely often in four dimensions, Electron. Comm. Probab.3 (1998) 35-42. Zbl0907.60063MR1637969
11. [11] J.-F. Le Gall, J. Rosen, The range of stable random walks, Ann. Probab.19 (1991) 650-705. Zbl0729.60066MR1106281
12. [12] R. Pemantle, Choosing a spanning tree for the integer lattice uniformly, Ann. Probab.19 (1991) 1559-1574. Zbl0758.60010MR1127715
13. [13] T. Salisbury, Energy, and intersections of Markov chains, in: Aldous D., Pemantle R. (Eds.), Random Discrete Structures, The IMA Volumes in Mathematics and its Applications, 76, Springer-Verlag, New York, 1996, pp. 213-225. Zbl0845.60068MR1395618
14. [14] D.B. Wilson, Generating random spanning trees more quickly than the cover time, in: Proceedings of the Twenty-eighth Annual ACM Symposium on the Theory of Computing (Philadelphia, PA, 1996), ACM, New York, 1996, pp. 296-303. Zbl0946.60070MR1427525
15. [15] W. Woess, Random Walks on Infinite Graphs and Groups, Cambridge Tracts in Math., 138, Cambridge University Press, Cambridge, 2000. Zbl0951.60002MR1743100