Continuum percolation: Frontmatter
Continuum percolation: Frontmatter
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连续体渗透：Frontmatter
DOI：
10.1017/cbo9780511895357
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发表时间：
1996
影响因子：
2
通讯作者：
R. Roy
中科院分区：
文献类型：
--
作者：
R. Meester;R. Roy
物理、化学和生物学中的许多现象都可以用空间随机过程来模拟。一个这样的过程是连续渗流，当被模拟的现象是由重叠的单个事件组成时，例如，单个雨滴最终使地面均匀湿润的方式。这是一个系统的连续渗流严格的帐户。详细讨论了两种模型：布尔模型和随机连接模型，并讨论了相关的连续模型。所有重要的技术和方法的解释和应用，以获得结果的存在相变，平等和连续性的临界密度，压缩，稀疏，和其他方面的连续模型。这种独立的治疗，假设只熟悉测量理论和基本概率论，将呼吁学生和研究人员在概率和随机几何。
Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry.