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eingereicht an der

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I declare that this thesis is my own account of my research and contains as its main content work which has not previously been submitted for a degree at any tertiary education institution.

Abstract. The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This ar-ticle reviews recent progress in the statistical modeling of spatial

belowground functioning of tropical biomes

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We study the generalizations of the well-known Lieb-Thirring inequality for the mag-netic Schrodinger operator with nonconstant magnetic eld. Our main result is the natu-rally expected magnetic Lieb-Thirring estimate on the moments of the negative eigenvalues for a certain class of magnetic elds (including even some unbounded ones). We develop a localization technique in path space of the stochastic Feynman-Kac representation of the heat kernel which eectively estimates the oscillatory eect due to the magnetic phase