论文标题
Riemannian歧管上的确定点过程的本地普遍性
Local universality of determinantal point processes on Riemannian manifolds
论文作者
论文摘要
我们考虑在光滑，紧凑的Riemannian歧管$（m，g）$上的Laplace-Beltrami操作员$Δ_g$和$-Δ_G$相关的$-Δ_G$相关的$-Δ_G$相关的$-Δ_G$相关的确定点过程$ \ MATHCAL {X}_λ$ on $ m $相关。我们表明，在适当的缩放下，$ \ Mathcal {x}_λ$的$ \ Mathcal {x}_λ$在适当的缩放下t_p^* m \ to m $ sybos t_p^* m $ as as $λ\ to \λ\ to \λ\ to \ from for f to \ from to \ infty $。
We consider the Laplace-Beltrami operator $Δ_g$ on a smooth, compact Riemannian manifold $(M,g)$ and the determinantal point process $\mathcal{X}_λ$ on $M$ associated with the spectral projection of $-Δ_g$ onto the subspace corresponding to the eigenvalues up to $λ^2$. We show that the pull-back of $\mathcal{X}_λ$ by the exponential map $\exp_p : T_p^*M \to M$ under a suitable scaling converges weakly to the universal determinantal point process on $T_p^* M$ as $λ\to \infty$.
