Geodesic
A lower bound for the affinity level for almost all Boolean functions
Diskretnaya Matematika, Tome 20 (2008) no. 4, pp. 85-88

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We consider the behaviour of the affinity level of the Boolean functions. It is shown that, as $n\to\infty$, almost all Boolean functions of $n$ variables have the affinity level exceeding $n-2\log_2n$. 
@article{DM_2008_20_4_a6,
     author = {O. A. Logachev},
     title = {A lower bound for the affinity level for almost all {Boolean} functions},
     journal = {Diskretnaya Matematika},
     pages = {85--88},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2008_20_4_a6/}
}
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O. A. Logachev. A lower bound for the affinity level for almost all Boolean functions. Diskretnaya Matematika, Tome 20 (2008) no. 4, pp. 85-88. http://geodesic.mathdoc.fr/item/DM_2008_20_4_a6/