BUSEMANN FUNCTIONS AND GIBBS MEASURES IN DIRECTED POLYMER MODELS ON Z2

• 成果类型: Article
• 署名作者: Janjigian, Christopher; Rassoul-Agha, Firas
• 署名单位: Utah System of Higher Education; University of Utah
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1375
• 发表日期: 2020
• 页码: 778-816
• 关键词: hamilton-jacobi equations; burgers-equation; semiinfinite geodesics; stationary solutions; fixed-points; coexistence; uniqueness; EXISTENCE; BEHAVIOR; systems

摘要

We consider random walk in a space-time random potential, also known as directed random polymer measures, on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices. We construct covariant cocycles and use them to prove new results on existence, uniqueness/nonuniqueness, and asymptotic directions of semi-infinite polymer measures (solutions to the Dobrushin-Lanford-Ruelle equations). We also prove nonexistence of covariant or deterministically directed bi-infinite polymer measures. Along the way, we prove almost sure existence of Busemann function limits in directions where the limiting free energy has some regularity.