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Spatial step edge fluctuations on a multi-component surface of Al/Si(111)-(root3 x root3) were measured via scanning tunneling microscopy over a temperature range of 720K-1070K, for step lengths of L = 65-160 nm. Even though the time scale of fluctuations of steps on this surface varies by orders of magnitude over the indicated temperature ranges, measured first-passage spatial persistence and survival probabilities are temperature independent. The power law functional form for spatial persistence probabilities is confirmed and the symmetric spatial persistence exponent is measured to be theta = 0.498 +/- 0.062 in agreement with the theoretical prediction theta = 1/2. The survival probability is found to scale directly with y/L, where y is the distance along the step edge. The form of the survival probabilities agree quantitatively with the theoretical prediction, which yields exponential decay in the limit of small y/L. The decay constant is found experimentally to be ys/L= 0.076 +/- 0.033 for y/L <= 0.2.
We study the distribution of first-passage functionals ${cal A}= int_0^{t_f} x^n(t), dt$, where $x(t)$ is a Brownian motion (with or without drift) with diffusion constant $D$, starting at $x_0>0$, and $t_f$ is the first-passage time to the origin. I
A well known connection between first-passage probability of random walk and distribution of electrical potential described by Laplace equation is studied. We simulate random walk in the plane numerically as a discrete time process with fixed step le
Levy walks (LWs) define a fundamental class of finite velocity stochastic processes that can be introduced as a special case of continuous time random walks. Alternatively, there is a hyperbolic representation of them in terms of partial probability
We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability $S(t)$ in equilibrium step fluctuations described by Langevin equations appropriate for attachment/detachment and edge-diffu
We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this process is non-stationary and its probability distribut