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Survival of the weak in hyperbolic spaces, a remark on competition and geometry
Author(s):
Itai
Benjamini
Journal:
Proc. Amer. Math. Soc.
130
(2002),
723-726.
MSC (1991):
Primary 30F45, 82C99
Posted:
July 25, 2001
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Abstract:
A simple competition model is presented. While in Euclidean spaces the weak will ``die out'', in the presence of hyperbolicity, coexistence take place.
References:
-
- 1.
- A. Ancona, (1988), Positive harmonic functions and hyperbolicity, LNM 1344 Springer, 1-23. CMP 21:05
- 2.
- J. Canon, W. Floyed, R. Kenyon, R. and W. Parry, (1997), Hyperbolic geometry, Math. Sci. Res. Inst. Publ. 31 59-115. MR 99c:57036
- 3.
- M. Gromov, (1987), Hyperbolic groups, Math. Sci. Res. Inst. Publ. 8, Springer, 75-263. MR 89e:20070
- 4.
- O. Häggström and R. Pemantle, (1998), First passage percolation and model for competing spatial growth, J. Appl. Prob. 35, 683-692. MR 2000f:60153
- 5.
- R. Pemantle (1990), A time-dependent version of Polya's urn, J. Theoret. Prob. 3 627-637. MR 91i:60030
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Additional Information:
Itai
Benjamini
Affiliation:
Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel 76100
Email:
itai@wisdom.weizmann.ac.il
DOI:
10.1090/S0002-9939-01-06077-4
PII:
S 0002-9939(01)06077-4
Received by editor(s):
May 20, 2000
Received by editor(s) in revised form:
August 25, 2000
Posted:
July 25, 2001
Communicated by:
Claudia M. Neuhauser
Copyright of article:
Copyright
2001,
American Mathematical Society
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