Recent developments in Random Walks: An LMS Durham Reseach Symposium

几十年来，随机游动一直是深入研究的对象，现在已经有了一个成熟的经典理论。它在概率论、组合学和分析中有着重要的意义，同时也在物理科学中有着广泛的应用。近年来，在这一领域取得了许多进展，推动了数学研究的发展，在一些新问题上取得了令人兴奋的进展。我们建议于2007年7月在达勒姆大学举行一次为期10天的会议，重点讨论随机介质中的随机游动和自相互作用的随机游动领域的问题。对随机介质中随机游动的兴趣源于对无序介质的物理性质的研究，其动机是在物理科学中的应用。具有自交互作用的随机行走是一种学习模型，其中行走的行为受到其过去历史的影响。这两个系统都带来了数学上的挑战，需要在更经典的领域，如群体上的随机游走进一步发展。这次会议的目的是汇集关键的研究人员，不仅从这些特定的领域，但从整个范围内的人工作的随机游走。会议将有一个整洁的讲座计划，有充分的机会进行讨论，合作和非正式会谈。我们的目标是确保所有人都意识到新技术和新挑战，这些都是我们关注的领域。通过汇集广泛的随机游走专家，这次会议将对这些丰富的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容易进入的网站分发，该网站将载有与会者名单、会谈摘要和其他有关信息。主要演讲将通过网络摄像头进行录制（经演讲者许可），并在会议结束后一个月内在网站上免费提供。课堂讲稿和/或幻灯片也将放在网站上。会议的更详细记录将通过在研究期刊上发表受会议所涉主题启发的前沿文章来提供。预计这次会议将为世界上随机游走理论的研究提供一个重大的持久的推动力。

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.