Weak limits of perturbed random walks and the equation $Y_t = B_t + \alpha\sup\{Y_s\colon s \leq t\}+\beta\inf\{Y\sb s\colon s \leq t\}$

On the matrix equations U_iXV_j W_{i j} for 1 \leq i; j \leq k with i +j \leq k

An $S$-adic characterization of minimal subshifts with first difference of complexity $1 \leq p(n+1) - p(n) \leq 2$

In [Ergodic Theory Dynam. System, 16 (1996) 663–682], S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is S-adic with Card(S) ≤ 327. In this paper, we improve this result by giving an S-adic charaterization of these subshifts with a set S of 5 morphisms, solving by this way the S-adic conjecture for this particular case.

Weak limits for quantum random walks.

We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With X(n) denoting position at time n, we show that X(n)/n converges weakly as n--> infinity to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain precedi...

An unbiased population-based search for the geometry optimization of Lennard-Jones clusters: 2 leq N leq 372

This article presents the results obtained using an unbiased Population Based Search (PBS) for optimizing Lennard-Jones clusters. PBS is able to repeatedly obtain all putative global minima, for Lennard-Jones clusters in the range 2 < or = N < or = 372, as reported in the Cambridge Cluster Database. The PBS algorithm incorporates and extends key techniques that have been developed in other Lenn...

The limits of Sinai ' s simple random walkin random

We study the sample path asymptotics of a class of recurrent diiusion processes with random potentials, including the examples of Sinai's simple random walk in random environment and Brox's diiusion process with Brownian potential. The main results consist of several integral criteria which completely characterize all the possible L evy classes, therefore providing a very precise image of the a...