41,901 research outputs found
Kazhdan-Lusztig polynomials and drift configurations
The coefficients of the Kazhdan-Lusztig polynomials are
nonnegative integers that are upper semicontinuous on Bruhat order.
Conjecturally, the same properties hold for -polynomials of
local rings of Schubert varieties. This suggests a parallel between the two
families of polynomials. We prove our conjectures for Grassmannians, and more
generally, covexillary Schubert varieties in complete flag varieties, by
deriving a combinatorial formula for . We introduce \emph{drift
configurations} to formulate a new and compatible combinatorial rule for
. From our rules we deduce, for these cases, the coefficient-wise
inequality .Comment: 26 pages. To appear in Algebra & Number Theor
Central Limit Theorem for Linear Statistics of Eigenvalues of Band Random Matrices
We prove the Central Limit Theorem for linear statistics of the eigenvalues
of band random matrices provided and test functions
are sufficiently smooth.Comment: minor revision; to appear in Random Matrices: Theory and Application
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