Self-Interacting Random Walks

本项目旨在研究一类定义在欧几里得格上的自相互作用过程的生长性质。该项目希望确定形状定理是否适用于一次增强随机漫步，并建立其递归/瞬态的条件。它还期望对简单随机漫步的局部时间获得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漫步领域长期存在的开放性问题，并为其研究开发新的方法。这不仅会给数学领域带来巨大的好处，也会给无数应用学科带来巨大的好处，这些学科都利用了自交互过程。

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.