Stochastic operators: properties and applications

Stochastic processes are widely used to model systems in which one or more variables fluctuate randomly. Problems arise when large sets of random variables are allowed to interact with each other, as is often the case with physical and biological systems. Stochastic operators provide a convenient framework for describing the interactions and evolution of the random variables. In this talk, I will discuss techniques and methods typically used in spin systems to deal with stochastic operators and their spectral analysis in the context of random processes. I will briefly review their properties and applications to biological systems. As practical examples, I will present some results of my research in infectious diseases and migration of glioma cells.