t for all xy y is coarsely embeddable CE a coarse embedding can be drawn in without excessive distortion many natural examples coarse equivalence of metric spaces similarly dened CE is a coarse property in case of a group or graph a coarse emb ID: 42222
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non-decreasing,propers.t.forallx,y#Z"!(d(x,y))$%f(x)&f(y)%$"+(d(,y))Ziscoarselyembeddable(CE)"'acoarseembeddingcanbedrawnin n),C )graphs!nwithgirthtendingtoinÞnitywhichareÔuniformlyÕCE:'"andfn:!n!!2s.t..x,y#!n"(d(x,y))$%fn(x)&fn(y)%2$d(x,y).ArelatedquestioninÞnitemetricspacegeometryis(Linial,Magen,Naor):