Sphere packings, codes, and kissing numbers via hard core models
Author(s)
Perkins, Will
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Abstract
We prove a lower bound on the expected size of a spherical code drawn from a "hard cap" model and the expected density of a packing drawn from the hard sphere model in high dimensions. These results allows us to improve the lower bound on the kissing number in high dimensions by a factor d and to prove new lower bounds on the entropy of sphere packings of density \Theta(d 2^{-d}) in R^d. Joint work with Matthew Jenssen and Felix Joos.
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Date
2018-05-17
Extent
32:51 minutes
Resource Type
Moving Image
Resource Subtype
Lecture