Balancing sums of random vectors

Balancing Sums of Random Vectors

We study a higher-dimensional ‘balls-into-bins’ problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to keep the sums of the vectors in the different bins close together; how close can we keep these sums almost surely? This question, our primary focus in this pap...

Asymptotics for dependent sums of random vectors

We consider sequences of length m of n-tuples each with k non-zero entries chosen randomly from an Abelian group or finite field. For what values of m does there exist a subsequence which is zero-sum or linearly dependent respectively? We report some results relating to these problems.

A Local Limit Theorem for Sums of Independent Random Vectors

We prove a local limit theorem for sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bounded.

Autoregressive Gaussian Random Vectors of First Order

Strong Laws for Weighted Sums of Negative Dependent Random Variables

In this paper, we discuss strong laws for weighted sums of pairwise negatively dependent random variables. The results on i.i.d case of Soo Hak Sung [9] are generalized and extended.