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- Gabrysch, Katja
(författare)
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On Directed Random Graphs and Greedy Walks on Point Processes
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of an introduction and five papers, of which two contribute to the theory of directed random graphs and three to the theory of greedy walks on point processes. We consider a directed random graph on a partially ordered vertex set, with an edge between any two comparable vertices present with probability p, independently of all other edges, and each edge is directed from the vertex with smaller label to the vertex with larger label. In Paper I we consider a directed random graph on ℤ2 with the vertices ordered according to the product order and we show that the limiting distribution of the centered and rescaled length of the longest path from (0,0) to (n, [na] ), a<3/14, is the Tracy-Widom distribution. In Paper II we show that, under a suitable rescaling, the closure of vertex 0 of a directed random graph on ℤ with edge probability n−1 converges in distribution to the Poisson-weighted infinite tree. Moreover, we derive limit theorems for the length of the longest path of the Poisson-weighted infinite tree. The greedy walk is a deterministic walk on a point process that always moves from its current position to the nearest not yet visited point. Since the greedy walk on a homogeneous Poisson process on the real line, starting from 0, almost surely does not visit all points, in Paper III we find the distribution of the number of visited points on the negative half-line and the distribution of the index at which the walk achieves its minimum. In Paper IV we place homogeneous Poisson processes first on two intersecting lines and then on two parallel lines and we study whether the greedy walk visits all points of the processes. In Paper V we consider the greedy walk on an inhomogeneous Poisson process on the real line and we determine sufficient and necessary conditions on the mean measure of the process for the walk to visit all points.
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| 2. |
- Villarroel, Beatriz
(författare)
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Active Galactic Nuclei in galaxy surveys : Empirical paths to the fiery hearts of cosmic beasts
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Some galaxies emit excessive amounts of light from their centers, caused by accretion of gas onto super-massive black holes (SMBH). These galactic cores are often referred to as Active Galactic Nuclei (AGN) and they come in many different forms, distinguishable by their emission properties. The AGN classes fall into two major categories: those with narrow Balmer lines, and those with broad Balmer lines. The AGN Unification theory of radio-quiet AGN predicts the two classes to differ mainly in the viewing angle of the observer who may, or may not, see the central engine due to dust obscuration in the foreground.In this PhD thesis, I explore the limits of the radio-quiet AGN Unification. In its most famous and simple form, the obscurer is a parsec-sized dust doughnut surrounding the accretion disk. I show that the galaxy neighbours to the two types of AGN are different, in disagreement with the simplest form of unification (Paper I). The two AGN classes differ in their [OIII]5007 luminosity, as well as in their star-formation history (Paper II), suggesting that we must incorporate galactic dust into the concept of AGN Unification, as well as differences in the luminosity of the central engine. I also present a novel, data-driven method to pinpoint the relative spatial origin of certain emission lines in AGN (Paper III). Finally, we conclude the thesis by discussing an anti-transient survey targeted at finding signatures of extra-terrestrial intelligence (Paper IV). This survey can, as a side effect, also be useful to find extreme, variable AGN that challenge both AGN Unification and evolutionary theories.
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