Research output: Contribution to journal › Article
A new approach to constant term identities and Selberg-type integrals. / Károlyi, G.; Nagy, Z.L.; Petrov, F.V.; Volkov, V.
In: Advances in Mathematics, Vol. 277, 2015, p. 252-282.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A new approach to constant term identities and Selberg-type integrals
AU - Károlyi, G.
AU - Nagy, Z.L.
AU - Petrov, F.V.
AU - Volkov, V.
PY - 2015
Y1 - 2015
N2 - Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. Built on a recent idea of Karasev and Petrov we develop a general interpolation based method that is powerful enough to establish many such identities in a simple manner. The main consequence is the proof of a conjecture of Forrester related to the Calogero–Sutherland model. In fact we prove a more general theorem, which includes Aomoto's constant term identity at the same time. We also demonstrate the relevance of the method in additive combinatorics.
AB - Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. Built on a recent idea of Karasev and Petrov we develop a general interpolation based method that is powerful enough to establish many such identities in a simple manner. The main consequence is the proof of a conjecture of Forrester related to the Calogero–Sutherland model. In fact we prove a more general theorem, which includes Aomoto's constant term identity at the same time. We also demonstrate the relevance of the method in additive combinatorics.
KW - Aomoto's constant term identity
KW - Calogero–Sutherland model
KW - Combinatorial Nullstellensatz
KW - Erdős–Heilbronn conjecture
KW - Forrester's conjecture
KW - Hermite interpolation
KW - Selberg integral
U2 - 10.1016/j.aim.2014.09.028
DO - 10.1016/j.aim.2014.09.028
M3 - Article
VL - 277
SP - 252
EP - 282
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
ER -
ID: 3979103