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Containing internal diffusion limited aggregation


 
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1. Title Title of document Containing internal diffusion limited aggregation
 
2. Creator Author's name, affiliation, country Hugo Duminil-Copin; Université de Genève; Switzerland
 
2. Creator Author's name, affiliation, country Cyrille Lucas; Université Paris 10; France
 
2. Creator Author's name, affiliation, country Ariel Yadin; Ben Gurion University; Israel
 
2. Creator Author's name, affiliation, country Amir Yehudayoff; Technion-IIT; Israel
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) IDLA, Random Walk, Percolation
 
3. Subject Subject classification 60G50; 60K35
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) The first author was supported by the EU Marie-Curie RTN CODY, the ERC AG CONFRA, as well as by the Swiss {FNS} and the Weizmann institute. The fourth author is a Horev fellow and is supported by the Taub Foundation, and by grants from ISF and BSF.
 
7. Date (YYYY-MM-DD) 2013-06-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2862
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2862
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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