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RESEARCH PRODUCT
Nonlocal random motions: The trapping problem
Piotr GarbaczewskiMariusz ŻAbasubject
PhysicsMesoscopic physicsQuantum PhysicsProperty (philosophy)Statistical Mechanics (cond-mat.stat-mech)General Physics and AstronomyFOS: Physical sciencesInterval (mathematics)Mathematical Physics (math-ph)Lévy processCauchy processMathematics::ProbabilityObstacleStatistical physicsQuantum Physics (quant-ph)Reference modelBrownian motionMathematical PhysicsCondensed Matter - Statistical Mechanicsdescription
L\'evy stable (jump-type) processes are examples of intrinsically nonlocal random motions. This property becomes a serious obstacle if one attempts to model conditions under which a particular L\'evy process may be subject to physically implementable manipulations, whose ultimate goal is to confine the random motion in a spatially finite, possibly mesoscopic trap. We analyze thisissue for an exemplary case of the Cauchy process in a finiteinterval. Qualitatively, our observations extend to general jump-type processes that are driven by non-gaussian noises, classified by the integral part of the L\'evy-Khintchine formula.For clarity of arguments we discuss, as a reference model, the classic case of the Brownian motion in the interval.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-12-23 |