It includes discrete and continuous random variables, their probability distributions and analytical and statistical methods for determining the mean, variance and higher order moments that ...

This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, Chernoff bounds and large deviations, martingales, ...

This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, martingales, concentration inequalities, branching ...

Invariance of a random discrete distribution under size-biased permutation is equivalent to a conjunction of symmetry conditions on its finite-dimensional distributions. This is applied to ...

The paper is devoted to a study of the exit boundary of random walks on discrete groups and related topics. We give an entropic criterion for triviality of the boundary and prove an analogue of ...