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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
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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 | References | Similar articles | Additional information

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

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J. Canon, W. Floyed, R. Kenyon, R. and W. Parry, (1997), Hyperbolic geometry, Math. Sci. Res. Inst. Publ. 31 59-115. MR 99c:57036

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M. Gromov, (1987), Hyperbolic groups, Math. Sci. Res. Inst. Publ. 8, Springer, 75-263. MR 89e:20070

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O. Häggström and R. Pemantle, (1998), First passage percolation and model for competing spatial growth, J. Appl. Prob. 35, 683-692. MR 2000f:60153

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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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