Verjetnostni izračun in statistika (Slovene)

The reserch program of the research group for probability and statistics has several components. - Cellular automata and interacting particle systems: Many physical processes display the phenomenon of self-organisation. The mathematical models for such phenomen make it possible to study aspects of these processes such as transitions from one equilibrium to another, effective perturbations, their spatial distribution and the propagation of supercritical droplets. Non-monotonic models are good starting point for the study of transitions between regular, fractal and chaotic dynamics. - Percolation: Here models of response to perturbations and the forming of global structures are studied. The theory has applications ranging from genetics to epidemiology where these models are used to study the effects of spatial or temporal constraints on the propagation of infections or specific genotypes. - Discrete structures and partial differential equations: the behaviour of systems on integer grids can in many cases be approximated by solutions of partial differential equations. This interaction provides new insights into the solutuions of PDEs on the one hand, and interacting particles on the other hand. - Mathematical finance: Derivative pricing and risk theory are an area of active research and one of the most visible applications of probability theory in recent years. Many questions regarding weather and energy derivatives are still largerly unresearched areas. - Time series: The series are a standard tool in statistics. However, new developments using stable processes have created a host of new questions on testing and filtering coming from either economics or engineering.