@article {IOPORT.05876937, author = {Janson, Svante and Ruci\'nski, Andrzej}, title = {Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs.}, year = {2011}, journal = {Arkiv f\"or Matematik}, volume = {49}, number = {1}, issn = {0004-2080}, pages = {79-96}, publisher = {Institut Mittag-Leffler, Djursholm; Springer, Dordrecht}, doi = {10.1007/s11512-009-0117-1}, abstract = {On a finite ground set of size $N$, a random subset is selected that independently includes each element with the same probability $p=p(N)$. Tail probabilities are estimated for the number of members of a given family of subsets that are included in the random subset. Close bounds are given for upper tail probabilities of edge counts in random hypergraphs. Applications to partition properties of random subsets of integers are considered. Rooted subgraphs of random graphs are investigated.}, reviewer = {Ove Frank (Stockholm)}, identifier = {05876937}, }