Critical exponents for a reversible nearest particle system on the binary tree

• 成果类型: Article
• 署名作者: Puha, AL
• 署名单位: California State University System; California State University San Marcos
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 395-415
• 关键词: contact process; triangle condition; homogeneous trees

摘要

The uniform model is a reversible interacting particle system that evolves on the homogeneous tree. Occupied sites become vacant at rate one provided the number of occupied neighbors does not exceed one. Vacant sites become occupied at rate beta times the number of occupied neighbors. On the binary tree, it has been shown that the survival threshold beta(c) is 1/4. In particular, for beta less than or equal to 1/4, the expected extinction time is finite. Otherwise, the uniform model survives locally. We show that the survival probability decays faster than a quadratic near beta(c). This contrasts with the behavior of the survival probability for the contact process on homogeneous trees, which decays linearly. We also provide a lower bound that implies that the rate of decay is slower than a cubic. Tools associated with reversibility, for example, the Dirichlet principle and Thompson's principle, are used to prove this result.