Let I be a finite index set and let B i , i # I, be events in a probability space. Let G be an undirected graph on vertex set I. Suppose that whenever J, K are disjoint subsets of I with no pairs j # J, k # K adjacent any Boolean expression of the B j , j # J is independent of any Boolean expression
โฆ LIBER โฆ
A useful elementary correlation inequality
โ Scribed by Ravi Boppona; Joel Spencer
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 85 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
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Let + be a Gaussian measure (say, on R n ) and let K, L R n be such that K is convex, L is a ``layer'' (i.e., L=[x: a (x, u) b] for some a, b # R and u # R n ), and the centers of mass (with respect to +) of K and L coincide. Then +(K & L) +(K) } +(L). This is motivated by the well-known ``positive