论文标题
$β$ -Dyson的布朗尼与布朗时代的布朗运动的同构
Isomorphisms of $β$-Dyson's Brownian motion with Brownian local time
论文作者
论文摘要
我们表明，高斯自由田地和对称马尔可夫的职业时间之间的Brydges-Fröhlich-Spencer-dynkin和Le Jan的同构，概括为$β$ -Dyson的Brownian Motion。对于$β\ in \ {1,2,4 \} $，这是高斯案例的结果，但是这种关系适用于一般$β$。我们进一步提出了一个问题，是否有$β$ -Dyson在一般电网上的布朗运动的类似物，在矩阵值估计的高斯自由场中插值和推断特征值领域。在$ n = 2 $的情况下，我们提供了一个简单的结构。
We show that the Brydges-Fröhlich-Spencer-Dynkin and the Le Jan's isomorphisms between the Gaussian free fields and the occupation times of symmetric Markov processes generalize to the $β$-Dyson's Brownian motion. For $β\in\{1,2,4\}$ this is a consequence of the Gaussian case, however the relation holds for general $β$. We further raise the question whether there is an analogue of $β$-Dyson's Brownian motion on general electrical networks, interpolating and extrapolating the fields of eigenvalues in matrix-valued Gaussian free fields. In the case $n=2$ we give a simple construction.
