Isoperimetric Problems in Discrete Spaces

By S. Bezrukov. 2002

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Phase transitions in phylogeny (2003, background): “By the isoperimetric inequality for the discrete cube [12] (see [15]; [ 3 ] for background) it follows that maximizers of the following quantity max{p : P[U] = P[U ′ ] = p; U, U ′ ⊂ {−1,1} d−1 and h(U, U ′ ) ≥ 2}”
A Brunn-Minkowski inequality for the integer lattice (2001, background): “There are many papers on this topic (see the survey of Bezrukov [ 2 ]).”