Benjamini-Schramm convergence and zeta functions

Benjamini-Schramm and spectral convergence

It is shown that under mild conditions, Benjamini-Schramm convergence of lattices in locally compact groups is equivalent to spectral convergence. Next both notions are extended to the relative case and are then expressed in terms of relative L2-theory.

算术局部对称空间的Benjamini-Schramm收敛

Benjamini--Schramm convergence of arithmetic locally symmetric spaces

该研究证明了算术局部对称空间的细部在体积中占比极小，并推导了其贝蒼潮数的渐进行为。

Benjamini-Schramm convergence of periodic orbits

We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation surfaces.

调和形式、Price不等式与Benjamini-Schramm收敛

Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence

本文利用Price不等式研究Benjamini-Schramm收敛到万有覆盖的Riemann流形序列的Betti数，分别在负Ricci曲率和负截面曲率条件下建立收敛结果，并通过精细Thick-Thin分解与Moser迭代去除离散性假设。

Coxeter polytopes and Benjamini--Schramm convergence

We observe that a large part of the volume of a hyperbolic polyhedron is taken by a tubular neighbourhood of its boundary, and use this to give a new proof for the finiteness of arithmetic maximal reflection groups following a recent work with M. Fraczyk and S. Hurtado. We also study in more depth the case of polygons in the hyperbolic plane.

高亏格平移曲面的 Benjamini-Schramm 极限：研究公告

Benjamini-Schramm limits of high genus translation surfaces: research announcement

本文证明面积等于亏格的 MSV 随机平移曲面在亏格趋于无穷时 Benjamini-Schramm 收敛于新引入的 Poisson 平移平面，并给出局部几何统计量的界。