Workshop: random structures and dynamics

Understanding the structure of random media, and the dynamics of processes associated with them, is crucial to many of the most fundamental applications of probability theory. Examples range from the modelling of substances with microscopic impurities in physics, to the description of the behaviour of networks with unpredictable connections between their nodes, arising in engineering and communications science.Such problems have been a stimulating source of mathematical challenges for many years, and the last decade has seen many rapid and significant developments. There is a pressing need for probabilists in the UK to be exposed to clear presentations of the emerging theory in this very active area of research. We propose a workshop centred around short lecture courses delivered by three experts in the area of random structures and their dynamics, along with a series of shorter individual talks by a range of experienced and upcoming researchers.The workshop will provide valuable opportunities for UK researchers to collaborate with experts visiting the workshop. It will also provide a mechanism for researchers with different perspectives coming from different areas of expertise to exchange ideas and techniques. We expect this to result in (a) further UK engagement in developing theory (b) investigations of new applications, and (c) new collaborations both within the UK probability community and between UK researchers and those working abroad.

The most direct beneficiaries of the workshop will be members of the UK probability community. The workshop will stimulate an increased engagement of these researchers in a very active and fast-moving area of research, as well as promoting collaborations within the UK and between UK researchers and those working abroad. Random structures and the dynamics associated with them are at the heart of many of the most important applications of probability theory in engineering, communications and computing. The mathematical structures discussed in the workshop have many applications in areas such as wireless communications, distributed computing, and remote sensing, particularly in the context of systems which need to be robust to attacks or to unpredictable outages. Similar challenges occur in the design and operation of transport networks, as well as in the control of epidemics. Many members of the UK probability community are involved in the application of theory in these contexts, both in collaboration with commercial partners and as advisers to governmental bodies such as GCHQ or the Department of Transport. Increased expertise of the UK community in these areas will deliver benefits to these commercial and governmental partners. The areas to be discussed in the workshop are a source of powerful modelling tools, and the development of the area will inevitably lead to benefits to those working in other academic and scientific disciplines. These are hard to predict, but one can give recent examples; for instance, the widespread use of models from random graph theory in research on social networks, and the remarkable success of techniques borrowed from statistical physics and the theory of disordered media in the development of algorithms for solving large combinatorial optimisation problems.