On Uniformly Random Discrete Interlacing Systems
Sammanfattning: This thesis concerns uniformly random discrete interlacing particle sys-tems and their connections to certain random lozenge tiling models. In par-ticular it contains the first derivation of a relatively unknown universal scalinglimit, which we call the Cusp-Airy process, of certain lozenge tiling modelsat a cusp point. In addition it contains a characterization of the geometryof the macroscopic behavior of uniformly random discrete interlaced parti-cle systems that, although not complete, shows many new and interestingfeatures.
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