标题： 高维超球面上的KPZ类似尺度 显示英文标题

标题： KPZ-like scaling on a high-dimensional hypersphere

摘要： 我们考虑由超球面拉普拉斯算子$\nabla^2_D$控制的取向扩散，在极限$D \to \infty$下，该算子位于$D$维超球面的表面。 我们发现，对于相对于超球面半径较短的拉伸路径，取向相关性的有限尺寸修正由Kardar-Parisi-Zhang (KPZ)标度指数$\gamma = 1/3$控制。 此外，我们对表示超球面表面的取向目标空间的拓扑结构进行了推测。 显示英文摘要

摘要： We consider the orientational diffusion controlled by the hyperspherical Laplacian, $\nabla^2_D$, on the surface of the $D$--dimensional hypersphere in the limit $D \to \infty$. We find that for stretched paths with lengths relatively short compared to the hypersphere's radius, the finite-size corrections in orientational correlations are controlled by the Kardar-Parisi-Zhang (KPZ) scaling exponent, $\gamma = 1/3$. In addition, we speculate about the topology of the orientational target space representing the surface of the hypersphere.