The box-crossing property for critical two-dimensional oriented percolation

• 成果类型: Article
• 署名作者: Duminil-Copin, H.; Tassion, V.; Teixeira, A.
• 署名单位: Universite Paris Saclay; University of Geneva
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0790-0
• 发表日期: 2018
• 页码: 685-708
• 关键词: contact process; 2 dimensions; critical probability; bounds; edge

摘要

We consider critical oriented Bernoulli percolation on the square lattice . We prove a Russo-Seymour-Welsh type result which allows us to derive several new results concerning the critical behaviorWe establish that the probability that the origin is connected to distance n decays polynomially fast in n. We prove that the critical cluster of 0 conditioned to survive to distance n has a typical width satisfying for some . The sub- linear polynomial fluctuations contrast with the supercritical regime where wn is known to behave linearly in n. It is also different from the critical picture obtained for non- oriented Bernoulli percolation, in which the scaling limit is non- degenerate in both directions. All our results extend to the graphical representation of the onedimensional contact process.