Recent developments in Random Walks: An LMS Durham Reseach Symposium

随机游走的最新进展：LMS Durham 研究研讨会

• 批准号: EP/E048595/1
• 负责人: John Bolton
• 金额: $ 8.97万
• 依托单位: Durham University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE048595%2F1
• 关键词: Recent; developments; Random; Walks; LMS

Random walks have been objects of intensive study over many decades with a well developed classical theory now in place. It has been a topic of importance in probability, combinatorics and analysis while having application across the physical sciences.In recent years there have been a number of advances in this area which have spurred on mathematical research, and we have seen exciting progress on some novel problems. We propose to hold a 10-day conference in July 2007 at Durham University, which will focus on problems in the area of random walks in random media and random walks with self-interaction. The interest in random walks in random media arose from the study of the physical properties of disordered media motivated by applications in the physical sciences. The random walk with self-interaction is a model for learning, in which the behaviour of the walk is influenced by its past history. Both systems bring mathematical challenges which necessitate further development in more classical areas such as random walks on groups.The aim of this meeting is to bring together key researchers not only from within these specific areas but from across the broad range of people working on random walks. The conference will have an uncluttered lecture programme, with ample opportunities for discussions, collaborations and informal talks. Our aim is to ensure that all are aware of new techniques and the new challenges that are arising for our areas of focus. By bringing together a broad range of random walk experts this meeting will have a significant impact on the development of these rich areas of research. The results of the meeting will be distributed initially via an actively-managed and easily accessible website, which will contain a list of participants, abstracts of talks and other relevant information. The main talks will be recorded (with permission of the speakers) via a web-cam, and be made freely available on the website within one month of the finish of the meeting. Lecture notes and/or slides will also be put on the site. A more detailed record of the meeting will be provided by the publication in research journals of cutting-edge articles inspired by the subjects covered in the meeting. The conference is expected to provide a major lasting fillip to world research in the theory of random walks.

几十年来，随机漫步一直是深入研究的对象，现在已经有了一个完善的经典理论。它在概率论、组合学和分析学中一直是一个重要的话题，同时在物理科学中也有应用。近年来，这一领域取得了许多进展，刺激了数学研究，我们在一些新问题上看到了令人兴奋的进展。我们拟于2007年7月在英国杜伦大学召开为期10天的会议，重点讨论随机媒体中的随机漫步问题和自交互随机漫步问题。对随机介质中的随机游走的兴趣源于对无序介质的物理性质的研究，并受到物理科学应用的激励。具有自我交互作用的随机行走是一种学习模型，在这种模型中，行走的行为受到其过去历史的影响。这两种系统都带来了数学上的挑战，需要在更经典的领域如群体随机漫步中进一步发展。这次会议的目的是汇集关键的研究人员，不仅来自这些特定领域，而且来自广泛的随机漫步研究人员。会议将有一个整洁的演讲计划，有充足的机会进行讨论、合作和非正式会谈。我们的目标是确保所有人都了解我们的重点领域正在出现的新技术和新挑战。通过汇集广泛的随机漫步专家，本次会议将对这些丰富研究领域的发展产生重大影响。会议的结果将首先通过一个积极管理和易于访问的网站分发，该网站将载有与会者名单、会谈摘要和其他相关信息。会议的主要内容将通过网络摄像头录下来（征得发言者的同意），并在会议结束后一个月内在网站上免费提供。课堂讲稿和/或幻灯片也会放在网站上。会议的更详细记录将通过在研究期刊上发表受会议主题启发的前沿文章来提供。这次会议有望为世界上随机漫步理论的研究提供一个重大而持久的推动力。