In recent decades the study of highly complex systems in biology, medicine, technology and industry and the associated micro-cosmic phenomena have given rise to the consideration of quantum effects in mathematical modeling outside the scope of quantum physics. Backed by leading physicists, prominent specialists in the field of brain research believe that the process of recognition with its accompanying classically inexplicable phenomena and paradoxes may only be described sufficiently well with the aid of quantum models. However, measurement processes, such as measuring brain activity through EEG or various forms of MRI, represent classical procedures that also can and should be treated with methods of classical statistics.
The major field of research for the Chair of Probability Theory and Mathematical Statistics is the investigation of quantum probabilistic phenomena and their relation to classical processes, especially point processes. In particular, through various international research projects in collaboration with partners in Jena, Rome and Tokyo, a number of possible models for a quantum statistical descriptions of the process of recognition were developed and the connection to classical statistical methods was shown.
Since 2002, the Chair is responsible for the publication of the book series "Quantum Probability and White Noise Analysis". During this period a total of 17 volumes were published by World Scientific Publishing. Furthermore, the Chair is significantly involved in the management of the Association for Quantum Probability and Infinite Dimensional Analysis (AQPIDA) comprising more than 100 scientists from this field of research.
In collaboration with the Centro Vito Volterra, University of Rome II, we are currently working on the development of statistical tests to verify the quality of random number generators. As a service to other departments of the University we offer statistical consulting.