Aspects and applications of the random walk
Aspects and applications of the random walk
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DOI：
10.1007/bf02179402
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发表时间：
1995-04
影响因子：
1.6
通讯作者：
J. Douglas
中科院分区：
文献类型：
--
作者：
J. Douglas
科学家们经常思考数学在描述复杂的合作现象时的”不合理的有效性”，这种现象发生在我们的物理环境中的许多尺度上----从亚原子到宇宙尺度的过程。这些数学模型的一个突出方面是控制方程的“普适性”，使得相同的数学框架可以包含对不同类型的材料性质和材料系统的准确描述。这种“普遍性”导致了许多“类比”，这往往使统计物理研究特别有趣。随机游走模型的成功，以及与这些游走相关的极限定理，描述了各种合作现象（相变，流体流动，.）的起源。同样值得注意的是，我们可以期待的观点和工具的随机游走理论提供线索的微观起源的大规模的自然界和成功的流体动力学数学模型引入描述动态和平衡合作现象。乔治韦斯提供了一个开始进入这个奇妙的领域的数学和物理调查。广泛适用的随机游走模型和有趣的数学随机游走理论，但是，导致了大量的文献随机游走这是广泛分散在技术和数学期刊。因此，学生很难在随机游走理论的数学方法和该理论的许多应用的概述中获得基本的基础。很好的总结随机游走理论存在这是专门为需要和利益的数学家，但没有类似的权威文本随机游走理论强调的倾向，一个物理科学家。韦斯的文本旨在缩小这一差距。他的书侧重于一个入门级的演示文稿打算为开始研究生与物理
Scientists have often pondered the" unreasonable effectiveness" of mathematics in describing the complex cooperative phenomena which occur at many scales in our physical environment--processes ranging from subatomic to cosmic dimensions. A striking aspect of these mathematical models is the" universality" of the governing equations such that the same mathematical framework can encompass an accurate description of diverse types of material properties and material systems. This" universality" leads to many" analogies" which often make statistical physics research especially interesting. The success of random walk models, and the limit theorems associated with these walks, in describing the origin of various kinds of cooperative phenomena (phase transitions, fluid flow,...) is similarly remarkable and we can expect the perspective and tools of random walk theory to offer clues into the microscopic origin of large-scale regularities in the natural world and into the success of hydrodynamic mathematical models introduced to describe dynamic and equilibrium cooperative phenomena. George Weiss offers an initiation into this wonderful area of mathematical and physical investigation.The wide applicability of random walk models and the interesting mathematics of random walk theory, however, have led to a large literature on random walks which is widely dispersed among technical and mathematical journals. Consequently, it is difficult for a student to obtain a basic grounding in the mathematical methods of random walk theory and an overview of the many applications of this theory. Good summaries of random walk theory exist which are tailored to the needs and interests of mathematicians, but there are no similar authoritative texts on random walk theory which emphasize the slant of a physical scientist. Weiss' text is targeted to reduce this gap. His book focuses on an introductory level presentation intended for the beginning graduate student with a physical