Timo Hirscher: Contraction method

Abstract:
Where discrete probability meets data science, i.e. in the area of random data structures and algorithms, there is often a natural way to subdivide a large problem into smaller instances of the same type (as the original one). This recursiveness, together with the idea of Banach's fixed-point theorem, can be used to get information about limiting distributions by means of rather elementary calculations - a tool, coined "contraction method", which became popular in the 90's and will be the topic of the seminar talk next week. After an introduction with help of hands-on examples I will try to sketch both its versatility and limitations.