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Examples ofisoperimetric
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This application depends on a new geometricisoperimetricinequality, showing that the conductance of small sets is actually better than the worst case bound.
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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.
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Since it is technically more cumbersome to work with surface areas, a version of theisoperimetricinequality expands this hypersurface into a full-dimensional set.
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Suchisoperimetricinequalities imply that a natural random walk on the graph converges rapidly to the uniform distribution on the vertices.
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There are two types ofisoperimetricinvariants which are often mentioned in the literature.
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We are not aware of anyisoperimetricinequality that would prove this conjecture.
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We derive improvedisoperimetricinequalities for discrete product measures on the ndimensional cube.
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The theorem and the approach used in its proof seem to provide convenient tools for dealing with a certain type ofisoperimetricstatements in the cube.
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Such a gap between the diameter and the mixing time cannot exist for vertex-transitive graphs or in graphs where theisoperimetricdimension is determined by the volume growth function.
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It should be noted that applying the aforementionedisoperimetricinequalities of [14, 2] would also yield similar exponential bounds of the 2 form e-u /2 (see [17]).
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Second, a hybrid approach is possible whereby the restrictions, for example, are analysed through path coupling and the projection is analysed by bounding someisoperimetricconstant for the chain.
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The simplest example is the infinite jungle gym, which has topological dimension 2 andisoperimetricdimension 3.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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