摘要翻译：
研究了描述二维无限双向高斯界面上给定点涨落的随机非马尔可夫过程h(t)从有界区间[-L,L]的首次退出时间的概率密度Q_t的长时间行为。我们证明当t\to\infty为幂律${-1-\alpha}时，Q_t衰减，其中\alpha是非普适的，与大小为L的涨落的热能和弹性能之比成正比。\alpha似乎依赖于L这一不同寻常的事实意味着Q_t存在的矩数依赖于窗口[-L,L]的大小。任意阶的矩作为L的函数，在足够小的L时存在，当L接近某个阈值L_n时发散，而在L>L_n时不存在。对于L>L_1，概率密度Q_t是可归一化的，但没有矩。
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英文标题：
《First-exit-time probability density tails for a local height of a
  non-equilibrium Gaussian interface》
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作者：
G.Oshanin (LPTMC, University of Paris 6, France)
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
  We study the long-time behavior of the probability density Q_t of the first exit time from a bounded interval [-L,L] for a stochastic non-Markovian process h(t) describing fluctuations at a given point of a two-dimensional, infinite in both directions Gaussian interface. We show that Q_t decays when t \to \infty as a power-law $^{-1 - \alpha}, where \alpha is non-universal and proportional to the ratio of the thermal energy and the elastic energy of a fluctuation of size L. The fact that \alpha appears to be dependent on L, which is rather unusual, implies that the number of existing moments of Q_t depends on the size of the window [-L,L]. A moment of an arbitrary order n, as a function of L, exists for sufficiently small L, diverges when L approaches a certain threshold value L_n, and does not exist for L > L_n. For L > L_1, the probability density Q_t is normalizable but does not have moments.
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PDF链接：
https://arxiv.org/pdf/801.3975