  This paper studies concentration inequalities for functions of locally
dependent random variables. We show that the usual definition of local
dependence does not imply concentration for general Hamming Lipschitz
functions. We define hypergraph dependence, which is a special case of local
dependence, and show that it implies concentration if the maximal neighborhood
size is small. We prove concentration in Hamming distance, Talagrand distance,
and for self-bounding functions of a particular type under this dependence
structure.
