Simulation of interpolating determinantal point processes

University essay from KTH/Matematik (Avd.)

Author: Philip Kennerberg; [2015]

Keywords: ;

Abstract:

In this master thesis I aim to present some of the basic theory of determinantal processes. Some preliminary theory of random measures and point-process theory is reviewed in the first chapter. In the second chapter I introduce the notion of a determinantal process, through what is called trace-class kernels. I mention a few of the most fundamental theorems from the field and go through some useful theorems for determinantal processes concerning interpolation between different processes. An algorithm for simulating determinantal processes was suggested earlier in [9]. I study this algorithm and derive more explicit formulas for implementation. The algorithm is however based on some assumptions that the underlying process is of a specific form. There is however a way to get around this assumption in order to study a wider class of processes, using another result from [9]. I will study some processes that interpolate between well-known processes, and use my implemented simulation tool to study how this interpolation manifests itself.

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