Steady-State L\'evy Flights in a Confined Domain
Abstract
We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric L\'evy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for L\'evy flights is derived and solved analytically in the steady state. It is shown that L\'evy flights are distributed according to the beta distribution, whose probability density becomes singular at the boundaries of the well. The origin of the preferred concentration of flying objects near the boundaries in nonequilibrium systems is clarified.
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