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Topics in Theoretical Computer Science : Internet Research Problems

Graduate · Historical course

Spring 2004 · Random Matrix Theory and Its Applications

Topics

  • Introduction
  • Matrix Jacobians (the 2x2 case)
  • Matrix Jacobians (the 2x2 case) (cont.)
  • Matrix Jacobians (the 3x3 case)
  • Matrix Jacobians and Spherical Coordinates
  • Matrix Jacobians with Wedge Products
  • Mechanics of Wedging
  • Plucker Coordinates
  • Jacobians of Matrix Factorizations
  • Jacobians of Matrix Factorizations (cont.)
  • Householder Transformations and the Stiefel Manifold
  • The Cauchy-Binet Theorem
  • Matrix Jacobians Interpreted Using the Cauchy-Binet Theorem
  • Telatar’s Paper and the Cauchy-Binet Theorem
  • Level Densities and the Cauchy-Binet Theorem
  • Orthogonal Polynomials
  • Matrix Integrals and Orthogonal Polynomials
  • Hypergeometric Functions of Matrix Arguments
  • Hypergeometric Functions of Matrix Arguments (cont.)
  • Computing Multivariate Orthogonal Polynomials Symbolically
  • Random Matrix Theory and Wireless Communications - I
  • Random Matrix Theory and Wireless Communications - II
  • Random Matrix Theory and Wireless Communications - III
  • Projects
  • Projects (cont.)
  • Advances and Open Research Areas in Random Matrix Theory

Readings

  • Random Growth Processes
    Listed reading
  • Proofs of Semicircle Law
    Listed reading
  • Random Matrices with Complex Eigenvalues
    Listed reading
  • Functions for Random Matrices
    Listed reading
  • Random Matrices and PCA
    Listed reading
  • Communication Theory
    Listed reading
  • Free Probability and Addition of Random Matrices
    Listed reading
  • Finite Fields
    Listed reading
  • Array Signal Processing
    Listed reading
  • Random Networks
    Listed reading
  • Random Graphs
    Listed reading
  • Computational Biology
    Listed reading
Spring 2002

Topics

  • Introduction
  • Routing Algorithms
  • Routing Algorithms (cont.)
  • DNS
  • Client-Server DNS
  • Load Balancing Problems (Regional)
  • Load Balancing Problems (Global)
  • Spring Break
  • Overlay Routing Networks
  • Streaming Content Delivery
  • TCP
  • Congestion Control
  • Coding, Compression, and Overlay Network
  • Geographically Distributed Applications
  • Visualization Tools
Sources