Random matrix theory thesis

Postfach D Bielefeld, Germany Closing date for applications is the

Random matrix theory thesis

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Mid-term Project

Multimodal data fusion is an interesting problem and its applications can be seen in image processing, signal processing and machine learning. In applications where we are given matrix data samples, for instance, adjacency matrices of networks or preference matrices from recommender matrices, it is desirable to extract trends from the data by using low rank representations of the matrices and finding low dimensional representations of the underlying entities.

Random matrix theory thesis

In this thesis, we shall be focussing our attention on the problem of multimodal data fusion with an interest in eigen value decomposition based algorithms. The contribution of this thesis is to introduce algorithms, that in a principled sense combine the samples to generate inferences about the underlying signal components by leveraging recent results from Random Matrix Theory.

The focus of our study would be to understand these algorithms in terms of phase transition boundaries, give sharp asymptotic bounds on the performance.

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We will then focus on the planted quasi clique recovery problem and discuss how could multiple independent network samples be used to generate an optimal inference about the clique structure in large networks.The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many pur- poses can (and perhaps should) be effectively studied in that level of generality.

Authors: Ryan Moulton, Yunjiang Jiang Download: PDF Abstract: We introduce simple, efficient algorithms for computing a MinHash of a probability distribution, suitable for both sparse and dense data, with equivalent running times to the state of the art for both benjaminpohle.com collision probability of these algorithms is a new measure of the similarity of .

In physics, random matrix theory is very useful to model a bunch of stuff, such as quantum gravity and heavy atomic nuclei. But we face a problem when trying to solve these models. Stability-based, random matrix theory filtering of financial portfolios Justin Daly Bachelor of Arts in Mathematics A Dissertation submitted in fulfillment of the.

1 Random Matrix Theory in the Press Since the beginning of the 20th century, Random matrix theory (RMT) has been finding applications in number theory, quantum mechanics, condensed matter physics, wireless communications, etc., see [16, 15, 12, 7].

Recently more and more disci-plines of science and engineering have found RMT valuable. Pages in category "Systems theory" The following pages are in this category, out of total. This list may not reflect recent changes ().

Projects | Infinite Random Matrix Theory | Mathematics | MIT OpenCourseWare