Computations of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix

The material on this webpage accompanies the article Computations of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix by Nobuki Takayama, Lin Jiu, Satoshi Kuriki and Yi Zhang.

Example1_HGM.nb, a Mathematica notebook for the demonstration of the holonomic gradient method for the evaluation of the expection of an Euler characteristic number. The notebook requires the availability of Koutschan's package HolonomicFunctions.m.

The following Mathematica files and notebooks are used in the section 5 of the article "Euler Characteristic Method for the Largest Eigenvalue of a Random Matrix":

• ec1_ann.nb, a Mathematica notebook for deriving a holonomic system of the integrand of the expectation of an Euler charateristic number.
  ec1_ann.m, the output of "ec1_ann.nb".
• ec1_ann1.nb, a Mathematica notebook for deriving a holonomic system of the inner single integral of the expectation of an Euler charateristic number.
  ec1_ann1.m, the output of "ec1_ann1.nb".
• ec1_ann2.nb, a Mathematica notebook for deriving a holonomic system of the inner double integral of the expectation of an Euler charateristic number.
  ec1_ann2.m, the output of "ec1_ann2.nb".
• ec1_ann3.nb, a Mathematica notebook for deriving a holonomic system of the inner triple integral of the expectation of an Euler charateristic number.
  ec1_ann3.m, the output of "ec1_ann3.nb".
• ec1_hgm.nb, a Mathematica notebook for the evaluation of the expectation of an Euler charateristic number by using the holonomic gradient method.

The following Mathematica files are D-finite (holonomic) systems of the inner double integral of the expectation of and Euler charateristics number without specifying parameters.

• ec1_ann2_1.m, a D-finite system of of the inner double integral of the expectation of and Euler charateristics number with one parameter.
• ec1_ann2_2.m, a D-finite system of of the inner double integral of the expectation of and Euler charateristics number with two parameters.
• ec1_ann2_3.m, a D-finite system of of the inner double integral of the expectation of and Euler charateristics number with three parameters.
• ec1_ann2_5.m, a D-finite system of of the inner double integral of the expectation of and Euler charateristics number with five parameters.