论文标题
非交换随机表面生长的三维高斯波动和反射壁
Three-dimensional Gaussian fluctuations of non-commutative random surface growth with a reflecting wall
论文作者
论文摘要
我们考虑了随机表面生长的多时间相关性和协方差结构，并在Arxiv中引入了壁：0904.2607。结果表明，与模型相关的相关函数沿空间样路径具有确定性结构，从而产生了高度波动的收敛，而高斯自由场的高度波动的收敛性。我们还构建了$ u（\ mathfrak {so} _ {n+1}）$上的连续时间非交互随机步行，当限制到$ u（\ mathfrak {so} _ {n+1}）时，该$匹配随机表面增长。作为应用程序，我们证明了矩与显式高斯自由场的收敛性，并沿着类似空间的路径和时间样路径获得相关随机点过程的协方差函数。特别是，它与Arxiv中重叠的随机WishArt矩阵的光谱中的三维高斯磁场不匹配：甚至沿着太空式路径，甚至甚至是2112.13728。
We consider the multi-time correlation and covariance structure of a random surface growth with a wall introduced in arXiv:0904.2607. It is shown that the correlation functions associated with the model along space-like paths have determinantal structure, which yields the convergence of height fluctuations to that of a Gaussian free field. We also construct a continuous-time non-commutative random walk on $U(\mathfrak{so}_{N+1})$, which matches the random surface growth when restricting to the Gelfand-Tsetlin subalgebra of $U(\mathfrak{so}_{N+1})$. As an application, we prove the convergence of moments to an explicit Gaussian free field and get the covariance functions of the associated random point process along both the space-like paths and time-like paths. In particular, it does not match the three-dimensional Gaussian field from spectra of overlapping stochastic Wishart matrices in arXiv:2112.13728 even along the space-like paths.
