Let X1, X2, ... , Xn be independent random variables such that ai ≤ Xi ≤ bi, i=1, 2, ..., n. A class of upper bounds on the probability P(S-ES ≤ nδ) is derived ...

Several important multivariate probability inequalities can be formulated in terms of multivariate convolutions of the form ∫ $f_{1}(x)f_{2}(x-\theta )dx$, where ...

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, ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...