Theses  Pure Mathematics and Mathematical Statistics
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A concentration inequality based statistical methodology for inference on covariance matrices and operators
(20170623)In the modern era of high and infinite dimensional data, classical statistical methodology is often rendered inefficient and ineffective when confronted with such big data problems as arise in genomics, medical imaging, ... 
Modern kNearest Neighbour Methods in Entropy Estimation, Independence Testing and Classification
(20171001)Nearest neighbour methods are a classical approach in nonparametric statistics. The knearest neighbour classifier can be traced back to the seminal work of Fix and Hodges (1951) and they also enjoy popularity in many other ... 
The Calderón problem for connections
(20171003)\indent\indent This thesis is concerned with the inverse problem of determining a unitary connection $A$ on a Hermitian vector bundle $E$ of rank $m$ over a compact Riemannian manifold $(M, g)$ from the DirichlettoNeumann ... 
Scaling limits of critical systems in random geometry
(20171001)This thesis focusses on the properties of, and relationships between, several fundamental objects arising from critical physical models. In particular, we consider SchrammLoewner evolutions, the Gaussian free field, ...