MOMENTS AND LYAPUNOV EXPONENTS FOR THE PARABOLIC ANDERSON MODEL

• 成果类型: Article
• 署名作者: Borodin, Alexei; Corwin, Ivan
• 署名单位: Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP944
• 发表日期: 2014
• 页码: 1172-1198
• 关键词: polymer

摘要

We study the parabolic Anderson model in (1 + 1) dimensions with nearest neighbor jumps and space time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we prove a contour integral formula for all moments and compute moment Lyapunov exponents of all orders.