CONVERGENCE IN LAW OF THE MINIMUM OF A BRANCHING RANDOM WALK

• 成果类型: Article
• 署名作者: Aidekon, Elie
• 署名单位: Eindhoven University of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP750
• 发表日期: 2013
• 页码: 1362-1426
• 关键词: limit-theorem; position; equation

摘要

We consider the minimum of a super-critical branching random walk. Addario-Berry and Reed [Ann. Probab. 37 (2009) 1041-1079] proved the tightness of the minimum centered around its mean value. We show that a convergence in law holds, giving the analog of a well-known result of Bramson [Mem. Amer Math. Soc. 44 (1983) iv+190] in the case of the branching Brownian motion.