Uniform convergence of spectral shift functions

一致收敛到 Airy 线系综

Uniform convergence to the Airy line ensemble

本文证明了最后到达渗流及相关不相交随机游走经典可积模型在紧集上一致收敛到 Airy 线系综，核心方法是通过证明不相交 Bernoulli 随机游走在参数空间所有可行方向上收敛，并利用耦合论证扩展至其他模型。

A Condition of Boshernitzan and Uniform Convergence in the Multiplicative Ergodic Theorem

This paper is concerned with uniform convergence in the multiplicative ergodic theorem on aperiodic subshifts. If such a subshift satisfies a certain condition, originally introduced by Boshernitzan, every locally constant SL(2,R)-valued cocycle is uniform. As a consequence, the corresponding Schrödinger operators exhibit Cantor spectrum of Lebesgue measure zero. An investigation of Boshernitzan's condition then shows that these results cover all earlier results of this type and, moreover, provide various new ones. In particular, Boshernitzan's condition is shown to hold for almost all circle …

Varadhan's decomposition of shift-invariant closed uniform forms for large scale interacting systems on general crystal lattices

We prove a uniform version of Varadhan decomposition for shift-invariant closed uniform forms associated to large scale interacting systems on general crystal lattices. In particular, this result includes the case of translation invariant processes on Euclidean lattices $\mathbf{Z}^d$ with finite range. Our result generalizes the result of arXiv:2009.04699 which was valid for systems on transferable graphs. In subsequent research, we will use the result of this article to prove Varadhan's decomposition of closed $L^2$-forms for large scale interacting systems on general crystal lattices.

量子积分 II：受控收敛与几乎一致收敛

Quantum integrals II: Dominated and almost uniform convergence

该研究在量子积分理论中构建了勒贝格受控收敛定理的非交换版本，还研究了非交换几乎一致收敛，建立了相关收敛概念间的联系。

正密度下从哈特里到弗拉索夫的半经典极限：强一致时间收敛和散射

The semiclassical limit from Hartree to Vlasov at positive density: strong uniform-in-time convergence and scattering

研究正密度下从哈特里方程到弗拉索夫方程的半经典极限，通过证明有限时间区间收敛速率并结合相关界，得到全局存在和散射，量子与经典初始扰动对齐时收敛一致且有显式速率。

Almost Sure Uniform Convergence of a Random Gaussian Field Conditioned on a Large Linear Form to a Non Random Profile

We investigate the realizations of a random Gaussian field on a finite domain of ${\mathbb R}^d$ in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and almost surely to a non random profile depending only on the covariance and the considered linear functional of the field. This is a significant improvement of the weaker $L^2$-convergence in probability previously obtained in the case of conditioning on a large quadratic functional.

Teleportation simulation of bosonic Gaussian channels: Strong and uniform convergence

We consider the Braunstein-Kimble protocol for continuous variable teleportation and its application for the simulation of bosonic channels. We discuss the convergence properties of this protocol under various topologies (strong, uniform, and bounded-uniform) clarifying some typical misinterpretations in the literature. We then show that the teleportation simulation of an arbitrary single-mode Gaussian channel is uniformly convergent to the channel if and only if its noise matrix has full rank. The various forms of convergence are then discussed within adaptive protocols, where the simulation …

Convergence of percolation on uniform quadrangulations with boundary to SLE$_{6}$ on $\sqrt{8/3}$-Liouville quantum gravity

Let $Q$ be a free Boltzmann quadrangulation with simple boundary decorated by a critical ($p=3/4$) face percolation configuration. We prove that the chordal percolation exploration path on $Q$ between two marked boundary edges converges in the scaling limit to chordal SLE$_6$ on an independent $\sqrt{8/3}$-Liouville quantum gravity disk (equivalently, a Brownian disk). The topology of convergence is the Gromov-Hausdorff-Prokhorov-uniform topology, the natural analog of the Gromov-Hausdorff topology for curve-decorated metric measure spaces. We also obtain analogous scaling limit results for fa…