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A Surface View of First-Passage Percolation

In: Proceedings of the International Congress of Mathematicians

Author

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  • Charles M. Newman

    (New York University, Courant Institute of Mathematical Sciences)

Abstract

Let $$\tilde B$$ (t) be the set of sites reached from the origin by time t in standard first-passage percolation on Z d , and let B0 (roughly lim $$\tilde B$$ (t)/t) be its deterministic asymptotic shape. We relate the t → ∞ microstructure of the surface of $$\tilde B$$ (t) to spanning trees of time-minimizing paths and their transverse deviations and to curvature properties of B0. The most complete results are restricted to d = 2.

Suggested Citation

  • Charles M. Newman, 1995. "A Surface View of First-Passage Percolation," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 1017-1023, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_94
    DOI: 10.1007/978-3-0348-9078-6_94
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