Recent developments in Random Walks: An LMS Durham Reseach Symposium

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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.