DUALITY BETWEEN COALESCENCE TIMES AND EXIT POINTS IN LAST-PASSAGE PERCOLATION MODELS

• 成果类型: Article
• 署名作者: Pimentel, Leandro P. R.
• 署名单位: Universidade Federal do Rio de Janeiro
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1044
• 发表日期: 2016
• 页码: 3187-3206
• 关键词: 2nd class particles; increasing subsequences; competition interfaces; directed polymers; fluctuations; geodesics; BEHAVIOR; GROWTH

摘要

In this article, we prove a duality relation between coalescence times and exit points in last-passage percolation models with exponential weights. As a consequence, we get lower bounds for coalescence times, with scaling exponent 3/2, and we relate its distribution with variational problems involving the Brownian motion process and the Airy(2) process. The proof relies on the relation between Busemann functions and the Burke property for stationary versions of the last-passage percolation model with boundary.