科研之友
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摘要
We consider a one-dimensional asymmetric random walk whose jumps are identical, independent and drawn from a distribution phi(eta) displaying asymmetric power-law tails (i.e. phi(eta) c/Tr+1 for large positive jumps and phi(eta) ('YITila+1) for large negative jumps, with 0 <alpha< 2). In the absence of boundaries and after a large number of steps n, the probability density PDF) of the walker position, x,, converges to an asymmetric Levy stable law of stability index a and skewness parameter,3 = ('y 1)/(-y + I). In particular, the right tail of this PDF decays as c n/x7Va. Much less is known when the walker is confined, or partially confined, in a region of the space. In this paper we first study the case of a walker constrained to move on the positive semi-axis and absorbed once it changes sign. In this case, the persistence exponent 0+, which characterizes the algebraic large time decay of the survival probability, can be computed exactly and we show that, if 0+ < 1, the tail of the PDF of the walker position decays as c n/[(1 0+) x7,1+1. This last result can be generalized in higher dimensions such as a two-dimensional random walker performing Levy stable jumps and confined in a wedge with absorbing walls. Our results are corroborated by precise numerical simulations.
- 出版日期2013-10
- 单位中国地震局
