Large deviations for truncated heavy-tailed random variables: a boundary   case
  This paper investigates the decay rate of the probability that the row sum of a triangular array of truncated heavy tailed random variables is larger than an integer (k) times the truncating threshold, as both - the number of summands and the threshold go to infinity. The method of attack for this problem is significantly different from the one where k is not an integer, and requires much sharper estimates. 
Arijit Chakrabarty
math.PR