Xia, Mingji

Title: About variable Lovasz local lemma

Abstract: Lovasz local lemma shows that given a dependency relation of random events, under which probabilities boundary, these events cannot cover the whole space. In the applications, the events are related, usually because they share random variables. In such a corresponding more specific variable-event dependency relation, the events maybe need higher probabilities to cover the whole space. For some cases we show the new probabilities boundary, to answer whether there is a gap between two boundaries.