摘要翻译：
本文将一维布朗运动(BMs)系统描述为:(i)Dyson BM模型，它是高斯么正系综(GUE)中厄米矩阵值扩散过程的特征值过程；(i)Weyl腔中吸收BM的H$变换，其中调和函数H$是变量差的乘积（Vandermonde行列式）。Karlin-McGregor公式给出了吸收BM跃迁概率密度的行列式表达式。本文从Karlin-McGregor公式出发，证明了当初始态处于GUE的特征值分布时，非冲突BM是一个行列式过程，即任意多时相关函数都是由矩阵核指定的行列式给出的。通过取适当的标度极限，导出了空间齐次和非齐次无限行列式过程。我们注意到与非碰撞粒子系统有关的行列式过程有一个共同的特征，即矩阵核是用适当的有效哈密顿量的谱投影来表示的。在矩阵核的公共结构上，证明了过程在时间上的连续性，并讨论了行列式过程的一般性质。
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英文标题：
《Noncolliding Brownian Motion and Determinantal Processes》
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作者：
Makoto Katori and Hideki Tanemura
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Physics        物理学
二级分类：Exactly Solvable and Integrable Systems        精确可解可积系统
分类描述：Exactly solvable systems, integrable PDEs, integrable ODEs, Painleve analysis, integrable discrete maps, solvable lattice models, integrable quantum systems
精确可解系统，可积偏微分方程，可积偏微分方程，Painleve分析，可积离散映射，可解格模型，可积量子系统
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英文摘要：
  A system of one-dimensional Brownian motions (BMs) conditioned never to collide with each other is realized as (i) Dyson's BM model, which is a process of eigenvalues of hermitian matrix-valued diffusion process in the Gaussian unitary ensemble (GUE), and as (ii) the $h$-transform of absorbing BM in a Weyl chamber, where the harmonic function $h$ is the product of differences of variables (the Vandermonde determinant). The Karlin-McGregor formula gives determinantal expression to the transition probability density of absorbing BM. We show from the Karlin-McGregor formula, if the initial state is in the eigenvalue distribution of GUE, the noncolliding BM is a determinantal process, in the sense that any multitime correlation function is given by a determinant specified by a matrix-kernel. By taking appropriate scaling limits, spatially homogeneous and inhomogeneous infinite determinantal processes are derived. We note that the determinantal processes related with noncolliding particle systems have a feature in common such that the matrix-kernels are expressed using spectral projections of appropriate effective Hamiltonians. On the common structure of matrix-kernels, continuity of processes in time is proved and general property of the determinantal processes is discussed.
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PDF链接：
https://arxiv.org/pdf/705.246