... fact will allowus to control both the entropy associated with the reflections and the changein the intersection volume caused by the reflections.7. Let xJ√N,Ndenote the shift through which ... its conditional expectation given a discreteskeleton. We do the same here. AbbreviateWi (c )=Waτ−1/(d−2)i,N (c ) ,i=1, 2,(2.9)V (c )=W1 (c ) ∩ W2 (c ) . ON THE VOLUME OF THE INTERSECTION ... −∞.(2.11)Proof. The crucial step is to apply a concentration inequality of Talagrandtwice, as follows. First note that, conditioned on Xi ,c ,ε, Wi (c ) is a union ofL = c /ε independent random sets. Call...