We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: D t u(t, x) = Bu + u · Ẇ , where D t is the Caputo fractional derivative of order α ∈ (0, 1) with respect to the time variable t, B is a second order elliptic operator with respect to the space variable x ∈ R and Ẇ a time homogeneous fractional ...

We present a novel method for exactly solving (in fact, counting solutions to) general constraint satisfaction optimization with at most two variables per constraint (e.g. MAX-2-CSP and MIN-2-CSP), which gives the first exponential improvement over the trivial algorithm. More precisely, the runtime bound is a constant factor improvement in the base of the exponent: the algorithm can count the n...

We consider the role of finite size effects on the value of the effective Hurst exponent H . This problem is motivated by the properties of the high frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer’s identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H = 1/2) i...

An early (and influential) scaling relation in the multifractal theory of diffusion limited aggregation (DLA) is the Turkevich-Scher conjecture that relates the exponent alpha(min) that characterizes the "hottest" region of the harmonic measure and the fractal dimension D of the cluster, i.e., D=1+alpha(min). Due to lack of accurate direct measurements of both D and alpha(min), this conjecture ...

The results of kinetic Monte Carlo simulations of epitaxial growth on fcc~100! and bcc~100! surfaces in which the correct crystal geometry is taken into account are reported. The existence of downward funneling to fourfold hollow sites leads to a downward current for large angles and to angle selection as observed in a variety of experiments. We have used our model to simulate Fe/Fe~100! deposi...

We investigate, in this paper, a number of magnetic properties of single and multilayer thin film systems within the Ising model by application of mean field, finite cluster approximations as well as by Monte Carlo simulations. The magnetization profiles and the magnetic ordering temperature are calculated for different magnetic systems. The influence of corrugation and disorder at the surface,...

Error exponents for single-user additive white Gaussian noise (AWGN) channels provide bounds on the rate of exponential decay of the average probability of error as a function of the block length of the random codebooks. In this paper, we only consider Gallager-type lower bounds of error exponents [1, 2]. For simplicity, we use the term “error exponent” to mean the maximum of random coding expo...

Loynes’ distribution, which characterizes the one dimensional marginal of the stationary solution to Lindley’s recursion, possesses an ultimately exponential tail for a large class of increment processes. If one can observe increments but does not know their probabilistic properties, what are the statistical limits of estimating the tail exponent of Loynes’ distribution? We conjecture that in b...