Complex analysis methods in noncommutative probability
Complex analysis methods in noncommutative probability
复制标题
非交换概率中的复杂分析方法
DOI：
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发表时间：
2006
期刊：
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通讯作者：
S. Belinschi
中科院分区：
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作者：
S. Belinschi
本文主要研究由非交换概率论引起的卷积。我们证明了自由卷积的几个正则性结果，以及部分定义的单参数自由卷积半群中的测度。在最后一章中，我们讨论了布尔卷积与自由卷积之间的联系，并证明了任何关于单调加性或乘性卷积的无限可分概率测度，相对于相应的卷积，都属于一个单参数半群。本论文部分结果的早期版本已经发表，而其他一些结果已经提交发表。我们几乎完全保留了印第安纳大学要求的博士论文的特定格式。这给文档增加了几个不必要的页面，但是我们希望保留文档作为印第安纳大学博士论文的特殊性。
In this thesis we study convolutions that arise from noncommutative probability theory. We prove several regularity results for free convolutions, and for measures in partially defined one-parameter free convolution semigroups. We discuss connections between Boolean and free convolutions and, in the last chapter, we prove that any infinitely divisible probability measure with respect to monotonic additive or multiplicative convolution belongs to a one-parameter semigroup with respect to the corresponding convolution. Earlier versions of some of the results in this thesis have already been published, while some others have been submitted for publication. We have preserved almost entirely the specific format for PhD theses required by Indiana University. This adds several unnecessary pages to the document, but we wanted to preserve the specificity of the document as a PhD thesis at Indiana University.