Selfishness of convex bodies and discrete point sets

2019 ◽  
Vol 80 ◽  
pp. 416-431
Author(s):  
Liping Yuan ◽  
Tudor Zamfirescu ◽  
Yue Zhang
Keyword(s):  
Convex Bodies ◽  
Discrete Point ◽  
Point Sets

Sampling inequalities for anisotropic tensor product grids

2019 ◽  
Vol 40 (1) ◽  
pp. 285-321
Author(s):  
Christian Rieger ◽  
Holger Wendland
Keyword(s):  
Tensor Product ◽  
Sparse Grid ◽  
Product Form ◽  
High Dimensional ◽  
Discrete Point ◽  
Point Sets ◽  
Stable Reconstruction ◽  
Anisotropic Tensor

AbstractWe derive sampling inequalities for discrete point sets that are of anisotropic tensor product form. Such sampling inequalities can be used to prove convergence for arbitrary stable reconstruction processes. As usual in the context of high-dimensional problems, our sampling inequalities are expressed in terms of the number of data sites, i.e., the number of points in the sparse grid. To this end, new bounds on specific monotone sets and on the number of points in an anisotropic sparse grid are derived.

scholarly journals Gibbs measures on permutations over one-dimensional discrete point sets

2015 ◽  
Vol 25 (2) ◽  
pp. 898-929 ◽  
Author(s):  
Marek Biskup ◽  
Thomas Richthammer
Keyword(s):  
Gibbs Measures ◽  
Discrete Point ◽  
Point Sets ◽  
One Dimensional
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