Alpha-Pfaffian, pfaffian point process and shifted Schur measure

Details Alpha-Pfaffian, pfaffian point process and shifted Schur measure Alpha-Pfaffian, pfaffian point process and shifted Schur measure

2004-11-12

arxiv.org/abs/math/0411277v2

Linear Algebra and its Applications 403 (2005) 369--398

Mathematics

Combinatorics

24 pages

Scientific paper

For any complex number $\alpha$ and any even-size skew-symmetric matrix $B$, we define a generalization $\pfa{\alpha}(B)$ of the pfaffian $\pf(B)$ which we call the $\alpha$-pfaffian. The $\alpha$-pfaffian is a pfaffian analogue of the $\alpha$-determinant. It gives the pfaffian at $\alpha=-1$. We give some formulas for $\alpha$-pfaffians and study the positivity. Further we define point processes determined by the $\alpha$-pfaffian. Also we provide a linear algebraic proof of the explicit pfaffian expression for the correlation function of the shifted Schur measure.

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