Random sub-algebras

The study of various abstract structures and their relations is one of the main concerns in mathematics. A well-known example of an algebraic structure is the real numbers. The objects are the numbers, and they satisfy certain relations to each other when applying multiplication or addition. Hence, there are rules that determine the relations between the objects, and this gives a structure. An operator algebra is a particular mathematical structure whose objects are maps (operators). In my project Random sub-Algebras", I will investigate a specific class of operator algebras with methods of probability theory. To apply randomness to deterministic structures has been quite fruitful in the past in mathematical research. To take a probabilistic viewpoint can open certain paths which are not visible in the deterministic regime. A commonly used method is to use random walks on the deterministic structure and investigate its long-term behaviour as time goes to infinity. This can give rise to an understanding of properties of the underlying structure. T h e a i m s o f m y p r o j e c t a r e , o n o n e h a n d , t o i