A multi-type shape theorem for FPP models

Abstract

An Euclidean first-passage percolation (FPP) model describing the competing growth between $k$ different types of infection is considered. We focus on the long time behavior of this multi-type growth process and we derive multi-type shape results related to its morphology.

Revised version with many corrections, 26 pages, 3 figures

References in corpus (3)

• Competition interfaces and second class particles
• Roughening and inclination of competition interfaces
• Asymptotics for first-passage times on Delaunay triangulations

Cited by in corpus (5)

• A phase transition for competition interfaces
• First passage percolation and competition models
• Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
• Shape of territories in some competing growth models
• Busemann functions and the speed of a second class particle in the rarefaction fan