On Choquet-Deny measures
On Chung-Teicher type strong law for arrays of vector-valued random variables.
On complete convergence for randomly indexed sums for a case without identical distributions.
On complete convergence in a Banach space.
On complete convergence of the sum of a random number of stable type random elements.
On concentrated probabilities
Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence such that for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff topological...
On concentrated probabilities on non locally compact groups
Let be a Polish group with an invariant metric. We characterize those probability measures on so that there exist a sequence and a compact set with for all .
On conditional expectations of vector valued variables
On conditions for the strong law of large numbers in general Banach spaces.
On continuous collections of measures
An integral representation theorem is proved. Each continuous function from a totally disconnected compact space to the probability measures on a complete metric space is shown to be the resolvent of a probability measure on the space of continuous functions from to .
On continuous convergence and epi-convergence of random functions. Part I: Theory and relations
Continuous convergence and epi-convergence of sequences of random functions are crucial assumptions if mathematical programming problems are approximated on the basis of estimates or via sampling. The paper investigates “almost surely” and “in probability” versions of these convergence notions in more detail. Part I of the paper presents definitions and theoretical results and Part II is focused on sufficient conditions which apply to many models for statistical estimation and stochastic optimization....
On continuous convergence and epi-convergence of random functions. Part II: Sufficient conditions and applications
Part II of the paper aims at providing conditions which may serve as a bridge between existing stability assertions and asymptotic results in probability theory and statistics. Special emphasis is put on functions that are expectations with respect to random probability measures. Discontinuous integrands are also taken into account. The results are illustrated applying them to functions that represent probabilities.
On convergence of infinitely divisible distributions in a Hilbert space
On convergence of series of random elements via maximal moment relations with applications to martingale convergence and to convergence of series with -orthogonal summands.
On convergence of series of random elements via maximal moment relations with applications to martingale convergence and to convergence of series with -orthogonal summands. Correction.
On d-finite tuples in random variable structures
We prove that the d-finite tuples in models of ARV are precisely the discrete random variables. Then, we apply d-finite tuples to the work by Keisler, Hoover, Fajardo, and Sun concerning saturated probability spaces. In particular, we strengthen a result in Keisler and Sun's recent paper.
On elliptic curves and random matrix theory
Rubinstein has produced a substantial amount of data about the even parity quadratic twists of various elliptic curves, and compared the results to predictions from random matrix theory. We use the method of Heegner points to obtain a comparable (yet smaller) amount of data for the case of odd parity. We again see that at least one of the principal predictions of random matrix theory is well-evidenced by the data.
On exceptional systems of random integers.
On factorization of probability distributions over directed graphs
Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple,...
On finite rank deformations of Wigner matrices
We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices under the assumption that the absolute values of the off-diagonal matrix entries have uniformly bounded fifth moment and the absolute values of the diagonal entries have uniformly bounded third moment. Using our recent results on the fluctuation of resolvent entries (On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, Unpublished...