Leonard N. Choup

Research Interests

My research interest lies in Random Matrix Theory (RMT) and Probability Theory. I am particularly interested in :

  • Distribution functions associated with the eigenvalues of random matrices.
  • Applications of Random Matrix to Statistics and growth processes.
  • Asymmetric Simple Exclusion Process.

Selected work

Abstracts and Presentations

  • L.N. Choup, Largest Eigenvalue in Random Matrix Theory. Joint Math Meeting University of Alabama, November 01, 2008
  • L.N. Choup, From Solitaire card games to the largest Eigenvalue through the Longest increasing subsequence. University of Alabama in Huntsville, February 22, 2008.
    • Abstract: We present the aspect of Random Matrix Theory dealing with the probability distribution functions of the largest eigenvalues. We introduce through the solitaire card game, an illustration of such distribution. This example closely related to the distribution of the length of the longest increasing subsequence in a random permutation enables us to make connections with the random matrix theory distribution functions.
  • L.N. Choup, Edge Scaling Correction, Gaussian and Laguerre Kernels for Unitary Ensembles. Presented at the SIAM Conference on Nonlinear Waves and Coherent Structures,University of Washington, Seattle, September 9-12 2006. 
    • Abstract: This paper discusses unitary ensembles of matrices, reporting on work involving edge scaling correction of Gaussian and Laguerre kernels.
  • L.N. Choup, Edgeworth Type Expansion of the distribution of the Largest Eigenvalue in Classical Random Matrix Ensembles. Presented at the Opening Workshop of the Program on High Dimensional Inference and Random Matrices, SAMSI, September 17-20, 2006. 
    • Abstract: We derive an edge scaling correction for Gaussian and Laguerre kernels for Unitary Ensembles, use it to write an expansion of F_{n,2}(t) = P(lambda_{max} < t) in terms of n in the first part,and give an outline of the steps needed to extend this analysis to the orthogonal and symplectic cases.
  • L.N. Choup, Semicircle low revisited, presented at the Research Focus Group in Random Matrices and Statistical Mechanics at University of California, Davis 2003-2004. 
    • Abstract: We present different proofs of the semicircle low.
  • L.N. Choup, Perron's Theorem and its applications, presented at the Student-Run Applied & Math Seminar at University of California, Davis. May 2005. 
    • Abstract: I will follow the wonderful paper of C. R. MacCluer: "The many proofs and applications of Perron's theorem."

Professional Development

  • UAHuntsville Southeastern session of the AMS, Co-Organizer of a special section on Random Matrix Theory. October 24-26 2008.
  • SAMSI Program on High Dimensional Inference and Random Matrices. Opening Workshop, September 17-20, 2006
  • SIAM Conference on Nonlinear Waves and Coherent Structures. University of Washington, Seattle, September 9-12, 2006
  • Courant Institute: Integrable Systems, Random Matrices and Applications, Courant Institute of Mathematical Sciences, New York, May 22-26, 2006.
  • CRM Summer School fellow for the "Random Matrices, Random Processes and Integrable Systems" program at the "Centre de Recherches Mathematiques" (CRM) Montreal Canada June 20 to July 8 2005