We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
"Conditional large and moderate deviations for sums of discrete random variables. Combinatoric applications." Bernoulli 18 (4) 1341 - 1360, November 2012. https://doi.org/10.3150/11-BEJ376