具有内自由度的二维Gibbsian粒子系统的平移不变性

二维Gibbsian点过程的平移不变性

Translation-invariance of two-dimensional Gibbsian point processes

具有相互作用的二维系统的平移对称守恒是统计力学的经典课题。在这里，我们建立了这样的结果与两体相互作用的吉布斯粒子系统，其中包括奇异的，硬核和不连续的相互作用的有趣的情况。我们从纯硬核排斥的特殊情况开始，以便说明如何一般地处理硬核。

Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles

We consider the ASEP and the stochastic six vertex model started with step initial data. After a long time, $T$, it is known that the one-point height function fluctuations for these systems are of order $T^{1/3}$. We prove the KPZ prediction of $T^{2/3}$ scaling in space. Namely, we prove tightness (and Brownian absolute continuity of all subsequential limits) as $T$ goes to infinity of the height function with spatial coordinate scaled by $T^{2/3}$ and fluctuations scaled by $T^{1/3}$. The starting point for proving these results is a connection discovered recently by Borodin-Bufetov-Wheeler…

Tightness of discrete Gibbsian line ensembles with exponential interaction Hamiltonians

In this paper we introduce a framework to prove tightness of a sequence of discrete Gibbsian line ensembles $\mathcal{L}^N = \{\mathcal{L}_k^N(x), k \in \mathbb{N}, x \in \frac{1}{N}\mathbb{Z}\}$, which is a collection of countable random curves. The sequence of discrete line ensembles $\mathcal{L}^N$ we consider enjoys a resampling invariance property, which we call $(H^N,H^{RW,N})$-Gibbs property. We also assume that $\mathcal{L}^N$ satisfies technical assumptions A1-A4 on $(H^N,H^{RW,N})$ and the assumption that the lowest labeled curve with a parabolic shift, $\mathcal{L}_1^N(x) + \frac{x^…

2DOCP无限体积极限点的DLR方程、数刚性与平移不变性

DLR equations, number-rigidity and translation-invariance for infinite-volume limit points of the 2DOCP

该研究证明任意正温度下二维单组分等离子体（2DOCP）的无限体积局部极限点满足DLR方程，还证明其极限过程具有数刚性与平移不变性，拓展了无限Ginibre系综的相关结果。

Equilibrium large deviations for mean-field systems with translation invariance

We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large deviation principles for its empirical measure at equilibrium. Our study covers the cases of McKean-Vlasov particle systems without external potential, and systems of rank-based interacting diffusions. Depending on the strength of the interaction, the large deviation principles are stated in the space of centered probability measures endowed with the Wasserst…

$g$的凸性、平移不变性和次可加性--期望和相关风险度量

Convexity, translation invariance and subadditivity for $g$-expectations and related risk measures

在发生器$g$上的连续假设下，Briand等人[Electron. Comm. Probab. 5（2000）101- 117]显示了$g$和条件$g$ -期望$({\mathcal{E}}_g[\cdot|{\mathcal{F}}_t])_{t\in[0,T]}$之间的某些联系，Rosazza Gianin [Insurance：Math.Econ.39（2006）19- 34]显示了$g$和相应的动态风险度量$(ρ^g_t)_{t\in[0,T]}$之间的某些联系。本文证明了在不对$g$作连续性假设的情况下，$g$ -期望${\mathcal{E}}_g$满足平移不变性的充要条件是$g$独立于$y$，且${\mathcal{E}}_g$满足凸性（分别为.次可加性）当且仅当$g$独立于$y$且$g$是凸的（分别次加性）相对于$z$。通过这些结论，我们推出了由$g$ -期望${\mathcal{E}}_g$诱导的静态风险度量$ρ^g$是凸的（分别为.一致）风险度量当且仅当$g$独立于$y$且$g$是凸的（分别为次线性）。我们的结果扩展了Briand等人[Electron. Comm. Probab. 5（2000）101- 117]和Rosazza Gianin [Insurance：Math.Econ.39（2006）19- 34]对这些主题的研究。