Numerical results for the directed polymer model in 1+4 dimensions in various types of disorder are presented. The results are obtained for a system size that is considerably larger than considered previously. For the extreme "strong" disorder case (min-max system), associated with the directed percolation model, the expected value of the meandering exponent, ζ=0.5, is clearly revealed, with ve...

In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with the finite sample behavior of the Hill estimator under α−stable distributions. Using large Monte Carlo simulations we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introdu...

The partition function pertaining to finite–temperature decoding of a (typical) randomly chosen code is known to have three types of behavior, corresponding to three phases in the plane of rate vs. temperature: the ferromagnetic phase, corresponding to correct decoding, the paramagnetic phase, of complete disorder, which is dominated by exponentially many incorrect codewords, and the glassy pha...

The partition function pertaining to finite–temperature decoding of a (typical) randomly chosen code is known to have three types of behavior, corresponding to three phases in the plane of rate vs. temperature: the ferromagnetic phase, corresponding to correct decoding, the paramagnetic phase, of complete disorder, which is dominated by exponentially many incorrect codewords, and the glassy pha...

Landau-Ginzburg mirror symmetry studies isomorphisms between graded Frobenius algebras, known as Aand B-models. Fundamental to constructing these models is the computation of the finite, Abelian maximal symmetry group Gmax W of a given polynomial W . For invertible polynomials, which have the same number of monomials as variables, a generating set for this group can be computed efficiently by i...

Renormalization group and scaling theory have been used to determine the large time growth exponent for the characteristic length, R(t), of an interface in the form R(t)∼ t. The exponent β is different in the two cases: quasi-static, in which the time derivative in the heat equation is suppressed, and the fully dynamic system. This paper examines the transition between the two regimes through a...

The security level of the achievability scheme for Wyner’s wiretap channel model is examined from the perspective of the probability of correct decoding, Pc, at the wiretap channel decoder. In particular, for finite–alphabet memoryless channels, the exact random coding exponent of Pc is derived as a function of the total coding rate R1 and the rate of each sub–code R2. Two different representat...

The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at criticality. The multifractal analysis of local measures is extended to more general observables including scaling variables such as the conductance in the localizat...

We investigate the critical properties of the d = 3 random-field Ising model with a Gaussian field distribution at zero temperature. By implementing suitable graph-theoretical algorithms, we perform a large-scale numerical simulation of the model for a vast range of values of the disorder strength h and system sizesV = L× L× L, with L 156. Using the sample-to-sample fluctuations of various quan...

The dominant Lyapunov exponent of a dynamical system measures the average rate at which nearby trajectories of a system diverge. Even though a positive exponent provides evidence for chaotic dynamics and upredictability, there may predictability of the time series over some finite time periods. In this paper one version of a local Lyapunov exponent is defined for a dynamic system perturbed by n...