探索Gillis模型：对数势中扩散的离散方法
Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials
摘要：
Gillis模型是60多年前提出的一种具有位置相关漂移的非齐次随机游动。虽然在物理和数学文献中引用得很少，但它提供了一个允许许多精确结果的随机系统的极少数例子之一，尽管缺乏平移不变性。我们提出了旧的和新的结果，这样的模型，而且我们表明，代表了离散版本的扩散粒子在对数势的存在下。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
