• Corpus ID: 232147041

Painlev\'{e} IV, $\sigma-$Form and the Deformed Hermite Unitary Ensembles

@inproceedings{Zhu2021PainleveI,
  title={Painlev\'\{e\} IV, \$\sigma-\$Form and the Deformed Hermite Unitary Ensembles},
  author={Mengkun Zhu and Dan Wang and Yang Chen},
  year={2021}
}
We study the Hankel determinant generated by a deformed Hermite weight with one jump w(z, t, γ) = e 2+tz|z − t|γ(A + Bθ(z − t)), where A ≥ 0, A + B ≥ 0, t ∈ R, γ > −1 and z ∈ R. By using the ladder operators for the corresponding monic orthogonal polynomials, and their relative compatibility conditions, we obtain a series of difference and differential equations to describe the relations among αn, βn, Rn(t) and rn(t). Especially, we find that the auxiliary quantities Rn(t) and rn(t) satisfy the… 
1 Citations
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