| 词汇 | isoperimetric |
| 释义 | BETA Examples of isoperimetricisoperimetric isn’t in the Cambridge Dictionary yet. You can help! This application depends on a new geometric isoperimetric inequality, showing that the conductance of small sets is actually better than the worst case bound. Finally, although it is not our focus here, let us briefly mention the question of edgeisoperimetric (as opposed to vertex-isoperimetric) inequalities for r-sets. Since it is technically more cumbersome to work with surface areas, a version of the isoperimetric inequality expands this hypersurface into a full-dimensional set. Such isoperimetric inequalities imply that a natural random walk on the graph converges rapidly to the uniform distribution on the vertices. There are two types of isoperimetric invariants which are often mentioned in the literature. We are not aware of any isoperimetric inequality that would prove this conjecture. We derive improved isoperimetric inequalities for discrete product measures on the ndimensional cube. The theorem and the approach used in its proof seem to provide convenient tools for dealing with a certain type of isoperimetric statements in the cube. Such a gap between the diameter and the mixing time cannot exist for vertex-transitive graphs or in graphs where the isoperimetric dimension is determined by the volume growth function. It should be noted that applying the aforementioned isoperimetric inequalities of [14, 2] would also yield similar exponential bounds of the 2 form e-u /2 (see [17]). Second, a hybrid approach is possible whereby the restrictions, for example, are analysed through path coupling and the projection is analysed by bounding some isoperimetric constant for the chain. The simplest example is the infinite jungle gym, which has topological dimension 2 and isoperimetric dimension 3. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. |
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