论文标题
探索吉利斯模型：一种离散的分散方法
Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials
论文作者
论文摘要
吉利斯（Gillis）模型于60多年前引入，是一个非均匀的随机步行，其位置依赖性漂移。尽管在物理和数学文献中都引用了简单的引用，但它提供了少数几个随机系统的例子之一，尽管缺乏翻译不变性，但允许许多确切的结果。我们为这种模型提供了旧的和新颖的结果，此外，我们表明的是在存在对数电位的情况下的扩散粒子的离散版本。
Gillis model, introduced more than 60 years ago, is a non-homogeneous random walk with a position dependent drift. Though parsimoniously cited both in the physical and mathematical literature, it provides one of the very few examples of a stochastic system allowing for a number of exact result, although lacking translational invariance. We present old and novel results for such model, which moreover we show represents a discrete version of a diffusive particle in the presence of a logarithmic potential.
