On the weak law of large numbers for normed weighted sums of i.i.d. random variables.
On transience conditions for Markov chains and random walks.
On Weak Tail Domination of Random Vectors
Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular then weak tail domination implies strong tail domination. In particular, a positive answer to Oleszkiewicz's question would follow from the so-called Bernoulli conjecture. We also prove that any unconditional logarithmically concave distribution is strongly dominated by a product symmetric exponential measure.
One-dimensional random walks, decreasing rearrangements and discrete Steiner symmetrization
Ordered random walks.
Ornstein-Metivier-Brunel theorem revisited