Alladi Ramakrishnan Hall

Growing patterns in the rotor-router model and the KPZ class

Rahul Dandekar

TIFR, Mumbai

The rotor-router model is a model of a deterministic walker which walks on a background configuration of arrows on a lattice. Its walk is dictated by the arrow configuration, which it also changes as it walks. Starting the walker from the origin on a given background, the boundary of the growing region explored by the walker upto time t, and the arrow configurations within this region, show interesting properties. On certain backgrounds which are random perturbations of periodic backgrounds, I will show that the growing boundaries of the pattern display Tracy-Widom fluctuations, and fall in the KPZ universality class.
References: (For periodic backgrounds)
arxiv.org/abs/1312.6888