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.
Project title: Trees and Central Limit Theorems
Area of research: Pure Mathematics, Geometric Group Theory
Fellowship period: 1 Oct 2021 - 30 Sep 2023
Fellowship type: AIAS-COFUND II Marie Skłodowska-Curie fellow
This fellowship has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 754513 and The Aarhus University Research Foundation.