  The spiked model is an important special case of the Wishart ensemble, and a
natural generalization of the white Wishart ensemble. Mathematically, it can be
defined on three kinds of variables: the real, the complex and the quaternion.
For practical application, we are interested in the limiting distribution of
the largest sample eigenvalue.
  We first give a new proof of the result of Baik, Ben Arous and P\'{e}ch\'{e}
for the complex spiked model, based on the method of multiple orthogonal
polynomials by Bleher and Kuijlaars. Then in the same spirit we present a new
result of the rank 1 quaternionic spiked model, proven by combinatorial
identities involving quaternionic Zonal polynomials (\alpha = 1/2 Jack
polynomials) and skew orthogonal polynomials.
  We find a phase transition phenomenon for the limiting distribution in the
rank 1 quaternionic spiked model as the spiked population eigenvalue increases,
and recognize the seemingly new limiting distribution on the critical point as
the limiting distribution of the largest sample eigenvalue in the real white
Wishart ensemble.
  Finally we give conjectures for higher rank quaternionic spiked model and the
real spiked model.

Probability;Classical Analysis and ODEs