We study Rademacher chaos indexed by a sparse set which has a fractional combinatorial dimension. We obtain tail estimates for finite sums and a normal limit theorem as the size tends to infinity. The tails for finite sums may be much larger than the tails of the limit.
"Rademacher chaos: tail estimates versus limit theorems." Ark. Mat. 42 (1) 13 - 29, April 2004. https://doi.org/10.1007/BF02432908