The shape theorem for the frog model

Annals of Applied Probability

Volumn 12, Issue 2, 2002, Pages 533-546

  Alves, O S M ^a   Machado, F P ^b   Popov, S Yu ^b  

^a FEDERAL UNIVERSITY OF GOIÁS   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Simple random walk; Subadditive ergodic theorem

Indexed keywords

EID: 0036338372     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1026915614     Document Type: Article

References (10)

1. BRAMSON, M. and GRIFFEATH, D. (1980). On the Williams-Bjerknes tumor growth model II. Math. Proc. Cambridge Philos. Soc. 88 339-357.
2. DURRETT, R. and GRIFFEATH, D. (1982). Contact processes in several dimensions. Z. Wahrsch. Verw. Gebiete 59 535-552.
3. DURRETT, R. and LIGGETT, T. M. (1981). The shape of the limit set in Richardson's growth model. Ann. Probab. 9 186-193.
4. HUGHES, B. D. (1995). Random Walks and Random Environments 1. Clarendon Press, Oxford.
5. KINGMAN, J. F. C. (1973). Subadditive ergodic theory. Ann. Probab. 1 883-909.
6. LAWLER, G. F. (1991). Intersections of Random Walks. Birkhäuser, Boston.
7. LIGGETT, T. M. (1985). An improved subadditive ergodic theorem. Ann. Probab. 13 1279-1285.
8. NAGAEV, S. V. (1979). Large deviations of sums of independent random variables. Ann. Probab. 7 745-789.
9. POPOV, S. YU. (2001). Frogs in random environment. J. Statist. Phys. 102 191-201.
10. TELCS, A., and WORMALD, N. C. (1999). Branching and tree indexed random walks on fractals. J. Appl. Probab. 36 999-1011.