Random Matrices, Combinatorics, Numerical Linear Algebra and Complex Networks

Abstract

Understanding large, random, matrices is important in many areas of interest to AFORS. These includes the probabilistic analysis of problems in numerical linear algebra, the efficiency of the simplex method in linear programming, the key parameters in statistical sampling, the expansion of complex networks such as the Internet graph, to mention a few. We have developed new methods with combinatorial flavor, combining tools from combinatorics, probability and high dimensional geometry to study several fundamental problems concerning random matrices, motivated by applications on complex networks and data analysis. Computer simulations also play an important role, serving as a guide for theoretical conjectures and as a check for approximations.

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Document Details

Document Type
Technical Report
Publication Date
Feb 16, 2012
Accession Number
ADA567088

Entities

People

  • Van H. Vu

Organizations

  • Rutgers University–New Brunswick

Tags

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Applied Mathematics
  • Biological Sciences
  • Computer Science
  • Contracts
  • Data Analysis
  • Data Science
  • Eigenvalues
  • Linear Algebra
  • Mathematics
  • Matrix Theory
  • Numerical Analysis
  • Probability
  • Random Variables
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Operations Research
  • Systems Analysis and Design