Two Gaussian measures are either mutually singular or equivalent. This dichotomy was first discovered by Feldman and Hajek (independently). We give a simple, almost formal, proof of this result, based on the study of a certain pair of functionals of the two measures. In addition we show that two Gaussian measures with zero means and smooth Polya-type covariances (on an interval) are equivalent ...

We determine the asymptotic behavior of the maximum subgraph density of large random graphs with a prescribed degree sequence. The result applies in particular to the Erdős-Rényi model, where it settles a conjecture of Hajek (1990). Our proof consists in extending the notion of balanced loads from finite graphs to their local weak limits, using unimodularity. This is a new illustration of the o...

Let {Yn, n≥ 1} be a sequence of nonmonotonic functions of associated random variables. We derive a Newman and Wright (1981) type of inequality for the maximum of partial sums of the sequence {Yn, n≥ 1} and a Hajek-Renyi-type inequality for nonmonotonic functions of associated random variables under some conditions. As an application, a strong law of large numbers is obtained for nonmonotonic fu...

In 2005 Li et al. gave a φ-competitive deterministic online algorithm for scheduling of packets with agreeable deadlines [12] with a very interesting analysis. This is known to be optimal due to a lower bound by Hajek [7]. We claim that the algorithm by Li et al. can be slightly simplified, while retaining its competitive ratio. Then we introduce randomness to the modified algorithm and argue t...