Jean-Rene Chazottes, Frank Redig, Evgeny Verbitskiy
We prove an exponential approximation for the law of approximate occurrence of typical patterns for a class of Gibssian sources on the lattice $\mathbb{Z}^d$, $d\ge2$. From this result, we deduce a law of large numbers and a large deviation result for the waiting time of distorted patterns.
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We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as $c\log n$, where $c$ is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our approach is based on the analysis of the first and second moment of the number of overlaps of a given size. We treat both the case of equal sequences (and nonzero shifts) and independent sequences.
Many Gibbs measures with mean field interactions are known to be chaotic, in the sense that any collection of $k$ particles in the $n$-particle system are asymptotically independent, as $n\to\infty$ with $k$ fixed or perhaps $k=o(n)$. This paper quantifies this notion for a class of continuous Gibbs measures on Euclidean space with pairwise interactions, with main examples being systems governed by convex interactions and uniformly convex confinement potentials. The distance between the marginal law of $k$ particles and its limiting product measure is shown to be $O((k/n)^{c \wedge 2})$, with …
Sampling from the Gibbs measure of the continuous random energy model and the hardness threshold
本文研究了连续随机能量模型（CREM）的 Gibbs 测度近似采样困难性阈值，证明了协方差函数凹与非凹情形下的算法运行时间界限，并给出了自由能下界。
Spectral gap bounds for reversible hybrid Gibbs chains
本文针对可逆混合Gibbs采样器收敛性质研究不足的问题，提出新方法建立其收敛速率界，证明混合Gibbs链绝对谱间隙可由精确链及近似用马尔可夫链的谱间隙界定，并拓展至混合数据增强算法，应用于三类采样器实例。
We obtain some approximation results for the weights appearing in the exchangeable partition probability function identifying Gibbs partition models of parameter $α\in (0,1)$, as introduced in Gnedin and Pitman (2006). We rely on approximation results for central and non-central generalized Stirling numbers and on known results for conditional and unconditional $α$ diversity. We provide an application to an approximate Bayesian nonparametric estimation of discovery probability in species sampling problems under normalized inverse Gaussian priors.
Approximate Gibbsian structure in strongly correlated point fields and generalized Gaussian zero ensembles
本文为强相关随机点场提出近似吉布斯结构的一般框架，并证明广义吉布斯性质对任意 $α$ 值的 $α$-GAFs 成立，从而确定其零点过程的刚性水平恰好为 $\lfloor \frac{1}{α} \rfloor$，解决了任意刚性水平点过程存在性的开放问题。
We show that under a low complexity condition on the gradient of a Hamiltonian, Gibbs distributions on the Boolean hypercube are approximate mixtures of product measures whose probability vectors are critical points of an associated mean-field functional. This extends a previous work by the first author. As an application, we demonstrate how this framework helps characterize both Ising models satisfying a mean-field condition and the conditional distributions which arise in the emerging theory of nonlinear large deviations, both in the dense case and in the polynomially-sparse case.
Using random graphs to sample repulsive Gibbs point processes with arbitrary-range potentials
本研究提出将排斥型Gibbs点过程归约为硬核模型的方法，通过生成随机几何图实现配分函数集中，可借助硬核模型算法采样与近似配分函数，为首款处理无界程对势的方法，并验证了算法性能与图的相关性质。
Disordered systems such as spin glasses have been used extensively as models for high-dimensional random landscapes and studied from the perspective of optimization algorithms. In a recent paper by L. Addario-Berry and the second author, the continuous random energy model (CREM) was proposed as a simple toy model to study the efficiency of such algorithms. The following question was raised in that paper: what is the threshold $β_G$, at which sampling (approximately) from the Gibbs measure at inverse temperature $β$ becomes algorithmically hard? This paper is a first step towards answering this…
Thermal Concentration and Poisson-Dirichlet Edge Statistics for Random-Lattice Gibbs Ensembles
研究高维Haar随机幺模格上的吉布斯测度，证明在边缘窗口内吉布斯质量的泊松点过程极限，并建立原始方向吉布斯系综的固定因子能见度曲线。
We continue our study of exponential law for occurrences and returns of patterns in the context of Gibbsian random fields. For the low temperature plus phase of the Ising model, we prove exponential laws with error bounds for occurrence, return, waiting and matching times. Moreover we obtain a Poisson law for the number of occurrences of large cylindrical events and a Gumbel law for the maximal overlap between two independent copies. As a by-product, we derive precise fluctuation results for the logarithm of waiting and return times. The main technical tool we use, in order to control mixing, …
Feasible approximation of matching equilibria for large-scale matching for teams problems
针对团队匹配问题，本文提出数值算法求解其近似最优解，可生成接近最优的近似匹配均衡，为决策者提供定量管理洞察，且次优性估计更保守性更低。
Griffiths inequalities and Gibbs-Bogoliubov inequality for general gauge glasses with Gaussian disorder on Nishimori line
研究在Nishimori线上具有高斯 disorder 的规范玻璃模型，证明了Griffiths不等式和Gibbs-Bogoliubov不等式，揭示了压力和关联函数随逆温度单调递增的性质。
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