Roughening and inclination of competition interfaces

Abstract

The competition interface between two growing ``Young clusters'' (diagrams), in a two-dimensional random cone, is mapped to the path of a second-class particle in the one-dimensional totally asymmetric simple exclusion process. Using the asymptotics of the second class particle and hydrodynamic limits for the exclusion process (Burgers equation), we show that the behavior of the competition interface depends on the angle of the cone: for angles in [180^o, 270^o) the competition interface has a deterministic inclination, while for angles in [90^o,180^o) the inclination is random. We relate the competition model to a model of random directed polymers, and obtain some partial results for the fluctuations of the competition interface.

4 pages, 3 figures

References in corpus (3)

• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Competition interfaces and second class particles
• The motion of a second class particle for the tasep starting from a decreasing shock profile

Cited by in corpus (6)

• A phase transition for competition interfaces
• A multi-type shape theorem for FPP models
• Scale invariant growth processes in expanding space
• Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
• On the collision between two PNG droplets
• Cube root fluctuations for the corner growth model associated to the exclusion process