The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthé, Holton, and Zamboni and the Diophan...

The probability that the cluster of the origin in critical site percolation on the triangular grid has diameter larger than R is proved to decay like R−5/48 as R→ ∞.

We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical nonlinearity in general, possibly non-smooth, bounded domains.

Short-time dynamic scaling behavior of the 3D ±J Ising spin glass is studied by Monte Carlo methods. Starting the replicas with independent initial configurations with a small pseudo magnetization, the dynamic evolution of the overlap q(t) between two replicas is measured. The initial increase of the overlap q(t) is observed and the corresponding exponent θ ′ is obtained. From the scaling relat...

Understanding the complex structure of karst networks is a challenge. In this work, we characterize the fractal properties of some of the largest coastal karst network systems in the world. They are located near the town of Tulum (Quintana Roo, Mexico). Their fractal dimension df , conductivity exponent μ̃ and walk dimension dw are estimated using real space renormalization and numerical simulat...

In this paper we study the on and off-equilibrium properties of the four dimensional Gaussian spin glass. In the static case we determine with more precision that in previous simulations both the critical temperature as well as the critical exponent. In the off-equilibrium case we settle the general form of the autocorrelation function, and show that is possible to obtain dynamically, for the f...

The purpose of this paper is to investigate spectral properties of the transition operator associated to a multivariate vector refinement equation and their applications to the study of smoothness of the corresponding refinable vector of functions. Let Φ = (φ1, . . . , φr) be an r× 1 vector of compactly supported functions in L2(IR) satisfying the refinement equation Φ = ∑ α∈Z s a(α)Φ(M · − α),...