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Suppose we are given a multi-dimensional It\^o process, which can be regarded as a model for an underlying asset price together with related stochastic processes, e.g., volatility. The drift and diff...
Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of the universe by leaving an imprint on the distribution of matter at late times. Much attention has been focused on using the ...
At low temperature in the epsilon regime of QCD the low-end of the Dirac spectrum is described by random matrix theory. In contrast, there has been no similarly well established staistical descriptio...
We present direct numerical simulations~(DNSs) of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements...
We study polytopes that are convex hulls of vectors of subgraph densities. Many graph theoretical questions can be expressed in terms of these polytopes, and statisticians use them to understand expon...
The phenomenon of Coulombic friction enters the stochastic description of dry friction between two solids and the statistic characterization of vibrating granular media. Here we analyze the correspon...
The Schrödinger equation for the evolution of isolated quantum systems determines the constants of motion for the dynamical problem, which can be identified with the populations along the princ...
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the...
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume ...
The application of Full Counting Statistics to a Dicke super-radiant model allows us to obtain an accurate description of the number of radiated bosons in the transient regime. This includes for examp...
Statistics of particles is one of the most fundamental aspects of quantum systems. Majorana fermions in vortices on a two-dimensional plane obey novel statistics called non-Abelian statistics. Non-Abe...
Quantum dynamics (e.g., the Schr\"odinger equation) and classical dynamics (e.g., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. The diff...
A method of radio frequency interference (RFI) suppression in radio astronomy spectral observations is described based on the analysis of the probability distribution of an instantaneous spectrum.
We study quantum walks of many non-interacting particles on a beam splitter array. Single as well as multi-mode counting statistics are obtained for generic input states. Bosonic interference e ects a...
We present a general scheme for treating particle beams, including stationary beams, as many particle systems. This includes the full counting statistics and the requirements of Bose/Fermi symmetry....

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