On extreme values in some random tessellation models

On extreme values in some random tessellation models.

I investigate several random mosaic models, most prominently β-Voronoi and β'-Voronoi, and establish some properties of their cells with respect to randomness. Chapter I describes geometry of the models and establishes independence of shape and size of typical n-faceted cell. Chapter II demonstrates that the maximal vertex degree in dual triangulations concentrates on a deterministic function if you restrict observation to a growing cubic window. And finally, Chapter III shows that the shape of typical cells tends to be close to specific families as we condition on the size being large.

Dissertation: https://hdl.handle.net/11370/25170ae2-61f5-47d3-8392-3a6dbc966203