arXiv subjects

Zhongkai Tao

Publications and source records attributed to Zhongkai Tao.

23 records · Page 2Linked to original sources

arXiv2023

Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds

We prove the convergence of the spectrum of the generator of the kinetic Brownian motion to the spectrum of the base Laplacian for closed Riemannian manifolds. This generalizes recent work of Kolb--Weich--Wolf [arXiv:2011.06434] on constant curvature surfaces and of Ren--Tao [arXiv:2208.13111] on locally symmetric spaces. As an application, we prove a conjecture of Baudoin--Tardif [arXiv:1604.06813] on the optimal convergence rate to the equilibrium.

math.SP↗

arXiv2022

Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces

We prove the strong convergence of the spectrum of the kinetic Brownian motion to the spectrum of base Laplacian for a large class of compact locally Riemannian homogeneous spaces, in particular all compact locally symmetric spaces. This generalizes recent work of Kolb--Weich--Wolf [arXiv:2011.06434] on constant curvature surfaces.

math.SP↗

arXiv2022

Flat trace estimates for Anosov flows

We prove a high energy flat trace estimate for the modified resolvent of the generator of an Anosov flow. This fills a gap in the proof of the local trace formula in [Jin-Zworski '17] and is a by-product of the authors' ongoing project of its generalization to Axiom A flows.

math.DS↗

arXiv2020

Exact Control for Schrödinger Equation on Torus

For standard torus $\mathbb{T}^2=\mathbb{R}^2/\mathbb{Z}^2$, we prove observability for free Schrödinger equation from a ball of radius $ε$ with explicit dependence of the observability constant on $ε$.

math.AP↗

arXiv2019

0-th Order Pseudo-differential Operator on the Circle

In this paper we consider 0-th order pseudodifferential operators on the circle. We show that inside any interval disjoint from critical values of the principal symbol, the spectrum is absolutely continuous with possibly finitely many embedded eigenvalues. We also give an example of embedded eigenvalues.

math.AP↗