Hitting probability of a distant point for the voter model started with a single 1

Annals of Probability

Volumn 36, Issue 3, 2008, Pages 807-861

  Merle, Mathieu ^a,b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Coalescing random walk; Hitting probability; Super brownian motion; Voter model

Indexed keywords

EID: 51949094381     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117907000000286     Document Type: Article

References (22)

1. d. Ann. Probat. 9 909-936. MR0632966
2. BRAMSON, M., COX, J. T. and LE GALL, J.-F. (2001). Super-Brownian limits of voter model clusters. Ann. Probab. 29 1001-1032. MR1872733
3. d. Z. Wahrsch. Verw. Gebiete 53 183-196. MR0580912
4. COX, J. T., DURRETT, R. and PERKINS, E. A. (2000). Rescaled voter models converge to super-Brownian motion. Ann. Probab. 28 185-234. MR1756003
5. CLIFFORD, P. and SUDBURRY, A. (1973). A model for spatial conflict. Biometrika 60 581-588. MR.0343950
6. DAWSON, D. A. (1975). Stochastic evolution equations and related measure-valued processes. J. Multivariate Anal. 3 1-52. MR0388539
7. DAWSON, D. A. (1993). Measure-valued Markov processes. Ecole d'Été de Probabilités de Saint-Flour XXI. Lecture Notes in Math. 15411-260. Springer, Berlin. MR1242575
8. DELMAS, J.-F. (1999). Some properties of the range of super-Brownian motion. Probab. Theory Related Fields 114 505-547. Springer, Berlin. MR1709279
9. DAWSON, D., ISCOE, I. and PERKINS, E. A. (1989). Super-Brownian motion: Path properties and hitting probabilities. Probab. Theory Related Fields 83 135-205. MR1012498
10. HOLLEY, R. A. and LIGGETT, T. M. (1975). Ergodic theorems for weakly interacting infinite systems and the voter model. Ann. Probab. 3 643-663. MR0402985
11. LAWLER, G. F. (1991). Intersections of Random Walks. Birkhauser, Boston. MR1117680
12. LE GALL, J.-F. (1997). Coalescing random walks, the voter model and super-Brownian motion. Personal communication.
13. LE GALL, J.-F. (1999). Spatial Branching Processes, Random Snakes and Partial Differential Equations. Birkhäuser, Boston. MR1714707
14. LE GALL, J.-F. (1994). A lemma on super-Brownian motion with some applications. In Festschrift in Honor of E. B. Dynkin (M. Friedlin, ed.) 237-251. Birkhäuser, Boston. MR1311723
15. LE GALL, J.-F. and PERKINS, E. A. (1995). The Hausdorff measure of the support of two-dimensional super-Brownian motion. Ann. Probab. 23 1719-1747. MR1379165
16. LIGGETT, T. M. (1985). Interacting Particle Systems. Springer, New York. MR0776231
17. LEDOUX, M. and TALAGRAND, M. (1991). Probability in Banach Spaces. Springer, New York. MR1102015
18. PERKINS, E. A. (1999). Dawson-Watanabe superprocesses and measure-valued diffusions. Lectures on Probability Theory and Statistics. Ecole d'Été de Probabilités de Saint-Flour XXIX. Lecture Notes in Math. 1781 125-324. Springer, Berlin. MR1915445
19. PERKINS, E. A. (1989). The Hausdorff measure of the closed support of super-Brownian motion. Ann. Inst. H. Poincaré Probab. Statist. 25 205-224. MR1001027
20. SAWYER, S. (1979). A limit theorem for patch sizes in a selectively-neutral migration model. J. Appl. Probab. 16 482-495. MR0540786
21. SPITZER, F. L. (1979). Principles of Random Walk. Springer, New York. MR03 88547
22. WATANABE, S. (1968). A limit theorem of branching processes and continuous state branching. J. Math. Kyoto Univ. 8 141-167. MR0237008