Inhomogeneous long-range percolation in the weak decay regime

• 成果类型: Article
• 署名作者: Moench, Christian
• 署名单位: Johannes Gutenberg University of Mainz
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01281-5
• 发表日期: 2024
• 页码: 1129-1160
• 关键词: uniqueness

摘要

We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several other previously investigated models. Our focus is on the weak decay regime, in which inter-cluster long-range connection probabilities fall off polynomially with small exponent, and for which we establish several structural properties. Chief among them are the continuity of the bond percolation function and the transience of infinite clusters.