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Interpretations of some parameter dependent generalizations of classical matrix ensembles
Peter J. Forrester, Eric M. Rains
Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolat…
Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter
Peter J. Forrester, Eric M. Rains
A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by…
A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces
A. R. Calderbank, R. H. Hardin, E. M. Rains +2
By using totally isotropic subspaces in an orthogonal space Omega^{+}(2i,2), several infinite families of packings of 2^k-dimensional subspaces of real 2^i-dimensional space are co…
The Shadow Theory of Modular and Unimodular Lattices
E. M. Rains, N. J. A. Sloane
It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24] +2, unless n = 23 when the bound must be increased by 1. This result was previously known only…
On Kissing Numbers in Dimensions 32 to 128
Yves Edel, E. M. Rains, N. J. A. Sloane
An elementary construction using binary codes gives new record kissing numbers in dimensions from 32 to 128.
A Simple Construction for the Barnes-Wall Lattices
G. Nebe, E. M. Rains, N. J. A. Sloane
A certain family of orthogonal groups (called "Clifford groups" by G. E. Wall) has arisen in a variety of different contexts in recent years. These groups have a simple definition…