The limiting shape for drifted internal diffusion limited aggregation is a true heat ball

• 成果类型: Article
• 署名作者: Lucas, Cyrille
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0505-0
• 发表日期: 2014
• 页码: 197-235
• 关键词: free-boundary; REGULARITY

摘要

We build the iDLA cluster using drifted random walks, and study the limiting shapes they exhibit, with the help of sandpile models. For constant drift, the normalised cluster converges to a canonical shape , which can be termed a true heat ball, in that it gives rise to a mean value property for caloric functions. The existence and boundedness of such a shape answers the natural yet open question of the existence and boundedness of a shape that satisfies a mean value property for caloric functions.