Self-Interacting Random Walks

本计画的目的是研究定义在欧几里德格上的一类自互动过程的成长性质。该项目旨在确定形状定理是否适用于一次强化的随机游动，并建立其复发/瞬态的条件。它还期望获得简单随机游动的局部时间的新的和非常精确的估计。该项目的预期成果包括解决强化随机行走领域长期存在的开放性问题，以及开发新的研究方法。这不仅对数学领域，而且对利用自交互过程的无数应用学科都将带来巨大的好处。

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.