Partial Survival and Crossing Statistics for a Diffusing Particle in a Transverse Shear Flow

Details Partial Survival and Crossing Statistics for a Diffusing Particle in a Transverse Shear Flow Partial Survival and Crossing Statistics for a Diffusing Particle in a Transverse Shear Flow

2006-09-27

arxiv.org/abs/cond-mat/0609710v1

J. Phys. A: Math. Gen. 39, L625 (2006)

Physics

Condensed Matter

Statistical Mechanics

4 pages

Scientific paper

10.1088/0305-4470/39/45/L01

We consider a non-Gaussian stochastic process where a particle diffuses in the $y$-direction, $dy/dt=\eta(t)$, subject to a transverse shear flow in the $x$-direction, $dx/dt=f(y)$. Absorption with probability $p$ occurs at each crossing of the line $x=0$. We treat the class of models defined by $f(y) = \pm v_{\pm}(\pm y)^\alpha$ where the upper (lower) sign refers to $y>0$ ($y<0$). We show that the particle survives up to time $t$ with probability $Q(t) \sim t^{-\theta(p)}$ and we derive an explicit expression for $\theta(p)$ in terms of $\alpha$ and the ratio $v_+/v_-$. From $\theta(p)$ we deduce the mean and variance of the density of crossings of the line $x=0$ for this class of non-Gaussian processes.

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