Discrete Probability

Abstract

In the last decades of the twientieth century an area has developed studying the properties and uses of large random structures. Probability naturally plays a central role in these investigations but it is probability of a somewhat special sort. First of all, the objects are finite. This removes questions of measurability that so bedevil many probabilists. Second of all, the objects are large. One is interested in the asymptotics as the size (here n) of the random object goes to infinity. Thus one is rarely interested [and can rarely obtain] exact forms for the relevant probabilities but instead is very interested in their asymptotics. Indeed, even the asymptotics can prove to be difficult in which case one struggles with improving lower and upper bounds.