Introduction to probability, random processes and basic statistical methods to address the random nature of signals and systems that engineers analyze, characterize and apply in their designs. It ...

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 ...

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 ...

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 ...

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, ...