Efficient simulation of rare events involving sums of heavy-tailed random variables has been an active research area in applied probability in the last fifteen years.
Lambert function is defined as the multivalued inverse relation of the function $f(w)=w\exp(w)$. We will study some of its important properties and prove some bounds.
Finding top k items and finding heavy hitters in data streams are two well studied problems in streaming algorithms. We shall discuss two deterministic streaming algorithms, one for each of these two problems.
