Date of Award


Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Physics (PhD)

Administrative Home Department

Department of Physics

Advisor 1

Alex Kostinski

Committee Member 1

Jacek Borysow

Committee Member 2

Will Cantrell

Committee Member 3

Vladimir Tonchev


The unifying theme of this thesis is the characterization of “perfect randomness,” i.e., independent and identically distributed (IID) stochastic processes as these are applied in physical science. Two specific and mathematically distinct applications are chosen: (i) Radar and optical polarimetry; (ii) Analysis of time series in meteorology. In (i), IID process of a special kind, namely, with a distribution defined by symmetry, is used to link its multivariate Gaussian density to uniformity on the Poincaré sphere. This “statistical ellipsometry” approach is then used to relate polarimetric mismatches or imbalances to ellipsometric variables and suitably chosen cross-correlation measures. In (ii), recently discovered and distribution-independent methods of data ranking are employed to examine temperature time series via the notion of the 2D cumulative distribution function in rank-time C(r, t) where the IID process again plays the central role in defining general signals. Several original analytic and computational results concerning C(r, t) are obtained.

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Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.