Outliers, the Law of Large Numbers, Index of Stability and Heavy Tails
  We are trying to give a mathematically correct definition of outliers. Our approach is based on the distance between two last order statistics and appears to be connected to the law of large numbers. Key words: outliers, law of large numbers, heavy tails, stability index. 
Lev B. Klebanov, Ashot V. Kakosyan and Andrea Karlova
math.PR math.ST stat.TH