Correlation functions for symmetrized increasing subsequences

By Eric M. Rains. 2000

115 citations recorded by the source corpus.

We show that the correlation functions associated to symmetrized increasing subsequence problems can be expressed as pfaffians of certain antisymmetric matrix kernels, thus generalizing the result of math.RT/9907127 for the unsymmetrized case.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/01d75dfffc4694613df22d3252b7981ea18c0cd9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Determinantal point processes (2018, background): “s. Let us list some Pﬀaﬁan analogs of the statements from the previous sections. • A Pfaﬃan analog of the Fredholm determinant formula (2.4) for the generating functional can be found in Section 8 of [Rai00]. • A Pfaﬃan analog of the Eynard-Mehta theorem is available in [Bor05]. • Pfaﬃans can be use”
The Ginibre Ensemble of Real Random Matrices and its Scaling Limits (2008, methodology): “A Pfaﬃan analog of the Cauchy-Binet formula introduced by Rains [20] lies at the heart of our proof.”
Universality of the Local Spacing Distribution¶in Certain Ensembles of Hermitian Wigner Matrices (2000, background): “See [ 27 ] for more results related to Proposition 2.2 below.”
Anyons in an exactly solved model and beyond (2005, unknown): “4 +a 14a 23 − a 13a 24. The Pfaﬃan satisﬁes the equations (Pf A)2 = detA, Pf(WAWT) = Pf(A) det(W). (137) We willalsoneed ageneralization ofthe Pfaﬃantoinﬁnite matrices, which iscalled Fredholm Pfaﬃan [75]. Let Aand Bbe real skew-symmetric, Binvertible, and A−Bhave a well-deﬁned trace. Then Pf(A,B) d”
Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs (2004, methodology): “roduced in [TW3]. The basic tool of our proofs is the computation of inverse of the “Gram matrix” of inner products for the corresponding model. Similar ideas have been previously used in [TW1], [B], [R], [J1], [J2], [J4]. In the last section of this paper we also discuss certain general properties ”
Universality of local eigenvalue statistics for some sample covariance matrices (2005, methodology): “5 in [31], for instance, the m-point correlation function of PT t is given by R N (x1, .”