Related papers: Fractal properties of the random string processes
A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…
We analyze here different types of fractional differential equations, under the assumption that their fractional order $\nu \in (0,1] $ is random\ with probability density $n(\nu).$ We start by considering the fractional extension of the…
In this work we are interested in the self--affine fractals studied by Gatzouras and Lalley and by the author which generalize the famous general Sierpinski carpets studied by Bedford and McMullen. We give a formula for the Hausdorff…
The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…
In this article, we identify the necessary and sufficient conditions for the existence of a random field solution for some linear s.p.d.e.'s of parabolic and hyperbolic type. These equations rely on a spatial operator $\cL$ given by the…
We study the asymptotic speed of a random front for solutions $u_t(x)$ to stochastic reaction-diffusion equations of the form \[ \partial_tu=\farc{1}{2}\partial_x^2u+f(u)+\sigma\sqrt{u(1-u)}\dot{W}(t,x),~t\ge 0,~x\in\Rm, \] arising in…
Consider an isotropic spherical Gaussian random field T with values in R^{d}. We investigate two problems: (i) When is the level set T^{-1}(t) nonempty with positive probability for any t\in R^{d} ? (ii) If the level set is nonempty, what…
The two most important notions of fractal dimension are {\it Hausdorff dimension}, developed by Hausdorff (1919), and {\it packing dimension}, developed by Tricot (1982). Lutz (2000) has recently proven a simple characterization of…
We find all the classical solutions (minimal surfaces) of open or closed strings in {\it any} two dimensional curved spacetime. As examples we consider the SL(2,R)/R two dimensional black hole, and any 4D black hole in the Schwarzschild…
We consider a class of random graphs, called random brushes, which are constructed by adding linear graphs of random lengths to the vertices of Z^d viewed as a graph. We prove that for d=2 all random brushes have spectral dimension d_s=2.…
The string propagation in the two-dimensional stringy black-hole is investigated from a new approach. We completely solve the classical and quantum string dynamics in the lorentzian and euclidean regimes. In the lorentzian case all the…
This paper discusses aspects of the second order hyperbolic partial differential equation associated with the ideal lossless string under tension and it's relationship to two discrete models. These models are finite differencing in the time…
An algorithm of searching a zero of an unknown undimensional function is considered, measured at a point x with some error. The step sizes are random positive values and are calculated according to the rule: if two consecutive iterations…
Consider a binary string $x$ of length $n$ whose Kolmogorov complexity is $\alpha n$ for some $\alpha<1$. We want to increase the complexity of $x$ by changing a small fraction of bits in $x$. This is always possible: Buhrman, Fortnow,…
Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…
For simplest colored branching processes we prove an analog to the McMillan theorem and calculate Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In…
Rare transitions in stochastic processes can often be rigorously described via an underlying large deviation principle. Recent breakthroughs in the classification of reversible stochastic processes as gradient flows have led to a connection…
We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which…
Let $\Theta=\{\theta_n\}, \Lambda=\{\lambda_n\}$ be two sequences of independent and identically distributed uniform random variables on $[0,1]$. The random vector-valued Weierstrass function is given by \[ f_{\Theta,\Lambda}(t)= \left(…
Fractional superstrings are non-trivial generalizations of ordinary superstrings and heterotic strings, and have critical spacetime dimensions which are less than ten by virtue of a worldsheet fractional supersymmetry relating worldsheet…