This dissertation presents some results from various areas of probability theory, the unifying theme being the use of functional analytic intuition and techniques. We first give a result regarding the existence of certain stochastic integral representations for Banach space valued Gaussian random variables. Next we give a spectral geometric construction...
We studied the problem of resource allocation in large scale distributed applications such as Online Social Networks (OSN) and Cloud Computing. In such settings, resource allocation schemes need to efficient as well as adaptive to the time-varying environments. The abstract resource allocation problem concerns with how to optimally use resources...
IC designers are continuously facing the challenges from reduced CMOS feature sizes and supply voltages. ADCs that deliver satisfactory resolutions/speeds while utilizing the state-of-the-art technologies to save power are in high demand. The analog circuits are more and more assisted by various digital calibration techniques to get boosted performances. This...
Frequency synthesizers are critical components of all communication systems. This thesis considers the issue of undesirable frequency spurs of a relatively recent type of frequency synthesis architecture called digital-to-time conversion (DTC). The DTC-based frequency synthesis architecture has important performance benefits over older frequency synthesizers, such as fast frequency switching, large...
Integral representations provide a useful framework of study and simulation of fractional Browian motion, which has been used in modeling of many natural situations. In this thesis we extend an integral representation of fractional Brownian motion that is supported on a bounded interval of ℝ to integral representation that is...
A comprehensive and scalable solution for high-performance switched capacitor amplification is presented. Central to this discussion is the concept of ring amplification. A ring amplifier is a small modular amplifier derived from a ring oscillator that naturally embodies all the essential elements of scalability. It can amplify with accurate rail-to-rail...
This thesis studies connections between disorder type in tree polymers and the branching random walk and presents an application to swarm site-selection. Chapter two extends results on tree polymers in the infinite volume limit to critical strong disorder. Almost sure (a.s.) convergence in the infinite volume limit is obtained for...