Quantum Probability and Spectral Analysis of Graphs
Quantum Probability and Spectral Analysis of Graphs
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DOI：
10.1007/3-540-48863-4
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发表时间：
2007-06
期刊：
影响因子：
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通讯作者：
A. Hora;尾畑 伸明
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文献类型：
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作者：
A. Hora;尾畑 伸明
我很高兴新的斯普林格量子概率程序由Hora Akihito和Nobuaki Obata的专著开启。事实上，这本书集中体现了当代量子概率的几个显着特点：首先，使用speci？c量子概率技术带来了原始的和相当不平凡的贡献的问题与一个古老的历史和大量的文献存在，都独立于量子概率。第二，但同样重要的是，在不同国家之间建立几座桥梁的能力？数学的各个分支显然彼此相距甚远，如正交多项式理论和图论，Nevanlinna的理论和对称群的表示理论。此外，主要议题的本专着，大图的渐近收敛性，正在获得越来越多的重要性，在多种应用中，几个不同的？erent？从固态物理到复杂网络，从生物学到生物学和操作研究，再到计算机优化。这是一个潜在的观众为目前的书，远远超出了数学家，包括物理学家，工程师的几个di？以及生物学家和经济学家。从数学的观点来看，使用复杂的分析工具对离散的结构（如图形）得出结论是特别有吸引力的。使用分析，科学的连续，发现n-平凡性质的离散结构已经建立了传统的数论，但在图论中，它构成了一个相对较新的趋势，几乎没有疑问，这一趋势将扩大到一个程度相媲美，我们？在数论中。量子概率的两个主要思想形成了本书的统一框架：1。经典随机变量的量子分解。
It is a great pleasure for me that the new Springer Quantum Probability ProgrammeisopenedbythepresentmonographofAkihitoHoraandNobuaki Obata. In fact this book epitomizes several distinctive features of contemporary quantum probability: First of all the use of speci? c quantum probabilistic techniques to bring original and quite non-trivial contributions to problems with an old history and on which a huge literature exists, both independent of quantum probability. Second, but not less important, the ability to create several bridges among di? erent branches of mathematics apparently far from one another such as the theory of orthogonal polynomials and graph theory, Nevanlinna’stheoryandthetheoryofrepresentationsofthesymmetricgroup. Moreover, the main topic of the present monograph, the asymptotic-haviour of large graphs, is acquiring a growing importance in a multiplicity of applications to several di? erent? elds, from solid state physics to complex networks, frombiologytotelecommunicationsandoperationresearch, toc-binatorialoptimization. Thiscreatesapotentialaudienceforthepresentbook which goes far beyond the mathematicians and includes physicists, engineers of several di? erent branches, as well as biologists and economists. From the mathematical point of view, the use of sophisticated analytical toolstodrawconclusionsondiscretestructures, suchas, graphs, isparticularly appealing. The use of analysis, the science of the continuum, to discover n-trivial properties of discrete structures has an established tradition in number theory, but in graph theory it constitutes a relatively recent trend and there are few doubts that this trend will expand to an extent comparable to what we? nd in the theory of numbers. Two main ideas of quantum probability form the unifying framework of the present book: 1. The quantum decomposition of a classical random variable.