6533b7cffe1ef96bd12584fd
RESEARCH PRODUCT
Cauchy flights in confining potentials
Piotr Garbaczewskisubject
Statistics and ProbabilityPhysicsQuantum PhysicsStationary distributionStatistical Mechanics (cond-mat.stat-mech)Stochastic processSemigroupMathematical analysisFOS: Physical sciencesCauchy distributionProbability density functionMathematical Physics (math-ph)Condensed Matter PhysicsLangevin equationLévy flightQuantum Physics (quant-ph)Representation (mathematics)Mathematical PhysicsCondensed Matter - Statistical Mechanicsdescription
We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process whose target pdf (eventually asymptotic) equals the preselected one. To this end, dynamically distinct jump-type processes can be employed. We demonstrate that one "targeted stochasticity" scenario involves Langevin systems with a symmetric stable noise. Another derives from the L\'evy-Schr\"odinger semigroup dynamics (closely linked with topologically induced super-diffusions), which has no standard Langevin representation. For computational and visualization purposes, the Cauchy driver is employed to exemplify our considerations.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-07-05 |