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- W2956073939 abstract "AbstractWe consider a semi-random walk on the space X of lattices in Euclidean n-space which attempts to maximize the sphere-packing density function Φ. A lattice (or its corresponding quadratic form) is called “sticky” if the set of directions in X emanating from it along which Φ is infinitesimally increasing has measure 0 in the set of all directions. Thus the random walk will tend to get “stuck” in the vicinity of a sticky lattice. We prove that a lattice is sticky if and only if the corresponding quadratic form is semi-eutactic. We prove our results in the more general setting of self-adjoint homogeneous cones. We also present results from our experiments with semi-random walks on X. These indicate some idea about the landscape of eutactic lattices in the space of all lattices." @default.
- W2956073939 created "2019-07-12" @default.
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- W2956073939 date "2019-06-26" @default.
- W2956073939 modified "2023-09-26" @default.
- W2956073939 title "Lattice-Packing by Spheres and Eutactic Forms" @default.
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- W2956073939 doi "https://doi.org/10.1080/10586458.2019.1624660" @default.
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