Geodesic
Spacings Between Integers Having Typically Many Prime Factors
Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 102-117

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DOI

We show that the sequence of integers which have nearly the typical number of distinct prime factors forms a Poisson process. More precisely, for $\delta$ arbitrarily small and positive, the nearest neighbor spacings between integers $n$ with $\left| \omega \left( n \right)\,-\,\log \log n \right|\,<\,{{\left( \log \log n \right)}^{\delta }}$ obey the Poisson distribution law.
DOI : 10.4153/CMB-2010-022-8
Mots-clés : 11K99 
Khan, Rizwanur. Spacings Between Integers Having Typically Many Prime Factors. Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 102-117. doi: 10.4153/CMB-2010-022-8
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     title = {Spacings {Between} {Integers} {Having} {Typically} {Many} {Prime} {Factors}},
     journal = {Canadian mathematical bulletin},
     pages = {102--117},
     year = {2010},
     volume = {53},
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     doi = {10.4153/CMB-2010-022-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-022-8/}
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