Survival of the weak in hyperbolic spaces, a remark on competition and geometry
HTML articles powered by AMS MathViewer
- by Itai Benjamini PDF
- Proc. Amer. Math. Soc. 130 (2002), 723-726 Request permission
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
- A. Ancona, (1988), Positive harmonic functions and hyperbolicity, LNM 1344 Springer, 1–23.
- James W. Cannon, William J. Floyd, Richard Kenyon, and Walter R. Parry, Hyperbolic geometry, Flavors of geometry, Math. Sci. Res. Inst. Publ., vol. 31, Cambridge Univ. Press, Cambridge, 1997, pp. 59–115. MR 1491098
- M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, DOI 10.1007/978-1-4613-9586-7_{3}
- Olle Häggström and Robin Pemantle, First passage percolation and a model for competing spatial growth, J. Appl. Probab. 35 (1998), no. 3, 683–692. MR 1659548, DOI 10.1239/jap/1032265216
- Robin Pemantle, A time-dependent version of Pólya’s urn, J. Theoret. Probab. 3 (1990), no. 4, 627–637. MR 1067672, DOI 10.1007/BF01046101
Additional Information
- Itai Benjamini
- Affiliation: Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel 76100
- MR Author ID: 311800
- Email: itai@wisdom.weizmann.ac.il
- Received by editor(s): May 20, 2000
- Received by editor(s) in revised form: August 25, 2000
- Published electronically: July 25, 2001
- Communicated by: Claudia M. Neuhauser
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 723-726
- MSC (1991): Primary 30F45, 82C99
- DOI: https://doi.org/10.1090/S0002-9939-01-06077-4
- MathSciNet review: 1866026