环面标度极限与 d ≥ 4 维临界弱耦合 |φ|⁴ 模型的平台效应

四维及更高维层级 $|φ|^4$ 模型的边界条件与两点函数平台

Boundary conditions and the two-point function plateau for the hierarchical $|φ|^4$ model in dimensions 4 and higher

本文在维度 d≥4 下证明了有限体积弱耦合层级 |φ|^4 模型两点函数在自由和周期边界条件下均存在平台，平台高度由与维度无关的 n 依赖普适剖面决定，并据此提出欧几里得模型的精确猜想。

Hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices

We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map. As we shall observe, the quasi-linear parabolic equation in the limit is defined on a flat torus and depends on both the local structure of the crystal lattice and the discrete harmonic map. We formulate the local ergodic theorem on the crystal lattice by introducing the notion of local function bundle, which is a family of local functions on the configuration space. The ideas and methods are taken from the discrete …

短程与长程弱耦合 $|φ|^4$ 模型在 $d \ge 4$ 临界点及其以上的重整化群映射

A Renormalisation Group Map for Short- and Long-ranged Weakly Coupled $|φ|^4$ Models in $d \ge 4$ at and Above the Critical Point

本文构造并分析了 $d \ge 4$ 维弱耦合 $|φ|^4$ 模型在周期边界条件下的重整化群映射，涵盖短程与长程相互作用，扩展了 Bauerschmidt 等人的工作，为确定关联函数精确衰减速率及有限体积系统中平台的出现提供了依据。

On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions

The objective of this article is to analyse the statistical behaviour of a large number of weakly interacting diffusion processes evolving under the influence of a periodic interaction potential. We focus our attention on the combined mean field and diffusive(homogenisation)limits. In particular, we show that these two limits do not commute if the mean field system constrained to the torus undergoes a phase transition, that is to say if it admits more than one steady state. A typical example of such a system on the torus is given by the noisy Kuramoto model of mean field plane rotators. As a b…

弱相互作用对数相关聚焦Gibbs测度的临界阈值

Critical threshold for weakly interacting log-correlated focusing Gibbs measures

研究了 $d$ 维环面上弱相互作用聚焦四次势的 log-correlated Gibbs measures，通过确定临界阈值展示了相变现象，并回答了 Brydges 和 Slade (1996) 提出的开放问题。

Weakly infinitely divisible measures on some locally compact Abelian groups

On the torus group, on the group of p-adic integers and on the p-adic solenoid, we give a construction of an arbitrary weakly infinitely divisible probability measure using a random element with values in a product of (possibly infinitely many) subgroups of the real numbers. As a special case of our results, we have a new construction of the Haar measure on the p-adic solenoid.

高维格点树与格点动物的近临界和有限尺寸标度

Near-critical and finite-size scaling for high-dimensional lattice trees and animals

针对上临界维度$d_{\rm c}=8$以上的$\boldsymbol{\text{Z}}^d$格点树和动物扩展模型，定义关联长度并证明其临界发散行为，推导近临界两点函数上界，研究环面系统的磁化率和两点函数平台特性，需扩展花边展开结果。

Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations

We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with transport type noises and $L^2$-initial data. Under a suitable scaling of the noises, we show that the solutions converge weakly to that of the deterministic 2D Navier--Stokes equations. Consequently, we deduce that the weak solutions of the stochastic 2D Euler equations are approximately unique and "weakly quenched exponential mixing".

弱扰动随机界面模型的尺度极限

Scaling Limits of a Weakly Perturbed Random Interface Model

该研究探讨了弱扰动随机界面模型在不同 γ 值下的尺度极限，揭示了其水动力方程和波动收敛性特性。

Scaling Limits for Stochastic SQG Equations and 2D Inviscid Critical Boussinesq Equations with Transport Noises

We study stochastic SQG equations on the torus $\mathbb{T}^2$ with multiplicative transport noise in the $L^2$-setting. Under a suitable scaling of the noise, we show that the solutions converge weakly to the unique solution to the deterministic dissipative SQG equation. A similar scaling limit result is proved also for the stochastic 2D inviscid critical Boussinesq equations.

带输运噪声与临界超线性扩散的反应扩散方程：弱耗散系统的全局适定性

Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems

该研究针对d维环面上带输运噪声的反应扩散系统，结合极大正则性、随机分析等工具，提出新的强制性条件与L^p(L^q)框架，证明了多类标量方程、耗散及弱耗散系统的全局适定性，部分无噪声情形结果也为新结论。