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A SHAPE THEOREM FOR RIEMANNIAN FIRST-PASSAGE PERCOLATION

Tom LaGatta, Jan Wehr

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Abstract

Abstract. Riemannian first-passage percolation (FPP) is a continuum analogue of standard FPP on the lattice, where the discrete passage times of standard FPP are replaced by a random Riemannian metric. We prove a shape theorem for this model— that balls in this metric grow linearly in time—and from this conclude that the metric is complete. 1.

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What this paper is about

Abstract. Riemannian first-passage percolation (FPP) is a continuum analogue of standard FPP on the lattice, where the discrete passage times of standard FPP are replaced by a random Riemannian metric. We prove a shape theorem for this model— that balls in this metric grow linearly in time—and from this conclude that the metric is complete. 1.

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Available abstract

Abstract. Riemannian first-passage percolation (FPP) is a continuum analogue of standard FPP on the lattice, where the discrete passage times of standard FPP are replaced by a random Riemannian metric. We prove a shape theorem for this model— that balls in this metric grow linearly in time—and from this conclude that the metric is complete. 1.

Key concepts: Fundamental theorem of Riemannian geometry, Mathematics, Riemannian geometry, Information geometry, Percolation (cognitive psychology), Metric (unit), Statistical manifold, Riemannian manifold

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