Sire C, Majumdar SN, Rudinger A
Laboratoire de Physique Quantique (UMR C5626 du CNRS), Universite Paul Sabatier, 31062, Toulouse Cedex, France.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Feb;61(2):1258-69. doi: 10.1103/physreve.61.1258.
In this paper, we present a detailed calculation of the persistence exponent straight theta for a nearly Markovian Gaussian process X(t), a problem initially introduced elsewhere in [Phys. Rev. Lett. 77, 1420 (1996)], describing the probability that the walker never crosses the origin. Resummed perturbative and nonperturbative expressions for straight theta are derived, which suggest a connection with the result of the alternative independent interval approximation. The perturbation theory is extended to the calculation of straight theta for non-Gaussian processes, by making a strong connection between the problem of persistence and the calculation of the energy eigenfunctions of a quantum mechanical problem. Finally, we give perturbative and nonperturbative expressions for the persistence exponent straight theta(X0), describing the probability that the process remains larger than X(0)sqrt[<X2(t)>].
在本文中，我们给出了近马尔可夫高斯过程(X(t))的持久指数(\theta)的详细计算，该问题最初在[《物理评论快报》77, 1420 (1996)]中其他地方被引入，描述了游走者从未穿过原点的概率。我们推导了(\theta)的重整化微扰和非微扰表达式，这表明它与替代独立区间近似的结果存在联系。通过在持久问题与量子力学问题的能量本征函数计算之间建立紧密联系，微扰理论被扩展到非高斯过程的(\theta)计算。最后，我们给出了持久指数(\theta(X_0))的微扰和非微扰表达式，它描述了过程保持大于(X(0)\sqrt{<X^2(t)>})的概率。
