9 papers
Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices
Cong Chen, Yong Li
We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift \(\frac{j(j-1)}{2}ω+ jy + x \mod 1\) for irrati…
Picard-Lefschetz theory and alien calculus: a case study
Si Li, Yong Li, Xinxing Tang
We compare Picard--Lefschetz theory and resurgence in three basic one-dimensional exponential integrals: the Airy model, the Bessel model, and the Gamma model. On the Picard--Lefsc…
Heat Kernel and Resurgence
Si Li, Yong Li, Xinxing Tang
We study the resurgent structure of short--time heat kernel asymptotics from the viewpoint of Picard--Lefschetz theory. For a real analytic Riemannian manifold, we show the heat ke…
Statistical Ensemble Deviation Estimates for Nearly Integrable Hamiltonian Systems
Xinyu Liu, Yong Li
This paper studies quantitative deviation bounds for statistical ensembles evolving under the one-parameter flow of a nearly integrable Hamiltonian system. Combining Nekhoroshev-ty…
Dyson Trace Flow and Multivariate Dynamic Coupled Semicircle Law
Cong Chen, Yong Li
Interacting random matrix systems are fundamental to modern theoretical physics and data science, yet a unified framework for their analysis has been lacking. This work introduces…
Resurgence for large expansion in Coulomb gas formalism
Yong Li, Hongfei Shu
We develop a resurgence analysis for large central charge (large ) expansions in two-dimensional CFTs using the Coulomb gas formalism. Through the exact Borel-Laplace representa…
KAM theory at the Quantum resonance
Huanhuan Yuana, Yong Li
We consider the semiclassical operator on , where the symbol of corresponds to a perturbed classi…
Semiclassical scar on tori in high dimension
Huanhuan Yuan, Yong Li
We show that the eigenfunctions of the self-adjoint elliptic differential operator exhibits semiclassical scar phenomena on the dimensional torus, under the -…
Quantum Birkhoff Normal Form in the -Bruno-Rüssmann non-resonant condition
Huanhuan Yuan, Yixian Gao, Yong Li
The aim of this paper is to construct a Gevrey quantum Birkhoff normal form for the -differential operator where , in the neighborho…