Enabling predictive mathematical modelling, the Law of Large Numbers (LLN) and Central Limit Theorem (CLT) from probability and statistics theory are key mathematical tools in many fields of Physics, Chemistry and Biology. LLN asserts that averages of sufficiently large number of random events tend to be representative of the underlying process. CLT is just the next, deeper level after LLN: averages of random events tend to be distributed accordingly to a very special probability measure, the normal distribution, informally seen as a `bell curve’.
The usual LLN and CLT (known from centuries) are stated for random events that are quantified as real numbers. However, to have better mathematical models it is more appropriate for the random events to take values in sets such as topological groups, manifolds, graphs, trees.... This project aims to explore CLT on new territories with random events taking values in metric trees and groups acting on them. Those are an important baby case for testing new techniques and ideas, as well as to give a solid foundation towards generalizing CLT to other groups and metric spaces.
Her field of research, called geometric group theory, is at the intersection of other Mathematical fields of research: harmonic analysis, ergodic theory, Lie theory and representation theory. For example, Lie theory aims to model the symmetries of our surrounding universe and is widely used in many areas of modern Mathematics and Physics. Beyond that, the Mathematical world is full of other types of symmetries. Her goal is to investigate those from a purely metric geometric point of view.