A pedestrian's view on interacting particle systems, KPZ universality, and random matrices

These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the basic physical concepts of equilibrium and nonequilibrium states, the one-dimensional simple exclusion process is introduced as a paradigmatic nonequilibrium interacting particle system. The stationary measure on the ring is derived and the idea of the hydrodynamic limit is sketched. We then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and explain the associated universality conjecture for surface fluctuations in growth models. This is followed by a detailed exposition of a seminal paper of Johansson that relates the current fluctuations of the totally asymmetric simple exclusion process (TASEP) to the Tracy-Widom distribution of random matrix theory. The implications of this result are discussed within the framework of the KPZ conjecture.Comment: 52 pages, 4 figures; to appear in J. Phys. A: Math. Theo

Reference programme: Diagnosis and treatment of headache disorders and facial pain. Danish Headache Society, 2nd Edition, 2012

Headache and facial pain are among the most common, disabling and costly disorders in Europe. Correct diagnosis and treatment is important for achieving a high quality of care. As a national organisation whose role is to educate and advocate for the needs of patients with primary headaches, the Danish Headache Society has set up a task force to develop a set of guidelines for the diagnosis, organisation and treatment of the most common types of headaches and for trigeminal neuralgia in Denmark. The guideline was published in Danish in 2010 and has been a great success. The Danish Headache Society decided to translate and publish our guideline in English to stimulate the discussion on optimal organisation and treatment of headache disorders and to encourage other national headache authorities to produce their own guidelines. The recommendations regarding the most common primary headaches and trigeminal neuralgia are largely in accordance with the European guidelines produced by the European Federation of Neurological Societies. The guideline provides a practical tool for use in daily clinical practice for primary care physicians, neurologists with a common interest in headache, as well as other health-care professionals treating headache patients. The guideline first describes how to examine and diagnose the headache patient and how headache treatment is organised in Denmark. This description is followed by individual sections on the characteristics, diagnosis, differential diagnosis and treatment of each of the major headache disorders and trigeminal neuralgia. The guideline includes many tables to facilitate a quick overview. Finally, the particular problems regarding headache in children and headache in relation to female hormones and pregnancy are described