On the strong law of large numbers on some ordered structures
On the strong laws for weighted sums of -mixing random variables.
On the weak law of large numbers for normed weighted sums of i.i.d. random variables.
On the weighted Euclidean matching problem in
A partitioning algorithm for the Euclidean matching problem in is introduced and analyzed in a probabilistic model. The algorithm uses elements from the fixed dissection algorithm of Karp and Steele (1985) and the Zig-Zag algorithm of Halton and Terada (1982) for the traveling salesman problem. The algorithm runs in expected time and approximates the optimal matching in the probabilistic sense.
One-dimensional finite range random walk in random medium and invariant measure equation
We consider a model of random walks on ℤ with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right Lyapunov eigenvectors of the random matrix naturally associated with the random walk, highlighting the mechanism of the model. This allows us to formulate a criterion for the existence of the absolutely continuous invariant measure for the environments seen from the particle. We then deduce a characterization...
Optimal bound for the discrepancies of lacunary sequences
The law of the iterated logarithm for discrepancies of lacunary sequences is studied. An optimal bound is given under a very mild Diophantine type condition.
Order Dentability and the Radon-Nikodym Property in Banach Lattices.