Hipster random walks

• 成果类型: Article
• 署名作者: Addario-Berry, L.; Cairns, H.; Devroye, L.; Kerriou, C.; Mitchell, R.
• 署名单位: McGill University; Cornell University; McGill University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-00980-z
• 发表日期: 2020
• 页码: 437-473
• 关键词: difference approximations

摘要

We introduce and study a family of random processes on trees we call hipster random walks, special instances of which we heuristically connect to the min-plus binary trees introduced by Robin Pemantle and studied by Auffinger and Cable (Pemantle's Min-Plus Binary Tree, 2017.[math.PR]), and to the critical random hierarchical lattice studied by Hambly and Jordan (Adv Appl Probab 36(3):824-838, 2004. 10.1239/aap/1093962236). We prove distributional convergence for the processes, after rescaling, by showing that their evolutions can be understood as a discrete analogues of certain convection-diffusion equations, then using a combination of coupling arguments and results from the numerical analysis literature on convergence of numerical approximations of PDEs.