Self-Interacting Random Walks

自交互随机游走

• 批准号: DP230102209
• 负责人: A/Prof Andrea Collevecchio
• 金额: $ 28.54万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-02-14 至 2026-02-13
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP230102209
• 关键词: Self; Interacting; Random; Walks

This project aims to study the growth properties of a class of self-interacting processes defined on Euclidean lattices. This project expects to determine whether a shape theorem holds for once-reinforced random walks, and establish conditions for their recurrence/transience. It also expects to obtain new and very precise estimates for the local time of simple random walks. Expected outcomes of this project include solving long-standing open problems in the field of reinforced random walks, and the development of novel methods for their study. This should provide significant benefits not only to the field of mathematics, but also to the myriad of applied disciplines where self-interacting processes are utilised.

该项目旨在研究欧几里得晶格上定义的一类自相互作用过程的生长特性。该项目期望确定形状定理对于一次强化随机游走是否成立，并为其重现/瞬态建立条件。它还期望获得简单随机游走的本地时间的新的且非常精确的估计。该项目的预期成果包括解决强化随机游走领域长期存在的开放性问题，以及开发新的研究方法。这不仅会给数学领域带来巨大的好处，而且也会给利用自交互过程的无数应用学科带来巨大的好处。