Work

Containing internal diffusion limited aggregation

Year: 2013

Type: article

Abstract: Internal Diffusion Limited Aggregation (IDLA) is a model that describes the growth of a random aggregate of particles from the inside out. Shellef proved that IDLA processes on supercritical percolation clusters of integer-lattices fill Euclidean balls, with high probability. In this article, we complete the picture and prove a limit-shape theorem for IDLA on such percolation clusters, by providing the corresponding upper bound. The technique to prove upper bounds is new and robust: it only requires the existence of a ``good'' lower bound. Specifically, this way of proving upper bounds on IDLA clusters is more suitable for random environments than previous ways, since it does not harness harmonic measure estimates.

Source: Electronic Communications in Probability

DOI: 10.1214/ecp.v18-2862

Authors: Hugo Duminil-Copin, Cyrille Lucas, Ariel Yadin, Amir Yehudayoff

Institutions: University of Geneva, Ben-Gurion University of the Negev, Technion – Israel Institute of Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Israel Science Foundation