Related papers: Normal approximation for Gibbs processes via disag…

In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space R^d are extended to the space of compact sets on R^d equipped by…

Graph Contrastive Learning (GCL) has emerged as a popular training approach for learning node embeddings from augmented graphs without labels. Despite the key principle that maximizing the similarity between positive node pairs while…

We examine the effect of clamping variables for approximate inference in undirected graphical models with pairwise relationships and discrete variables. For any number of variable labels, we demonstrate that clamping and summing approximate…

We discuss the general link between mode-coupling like equations (which serve as the basis of some recent theories of supercooled liquids) and the dynamical equations governing mean-field spin-glass models, or the dynamics of a particle in…

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term…

The rapid proliferation of large language models and natural language processing (NLP) applications creates a crucial need for uncertainty quantification to mitigate risks such as hallucinations and to enhance decision-making reliability in…

We study the fluctuations of the eigenvalues of real valued large centrosymmetric random matrices via its linear eigenvalue statistic. This is essentially a central limit theorem (CLT) for sums of dependent random variables. The dependence…

We establish central limit theorems (CLTs) for the linear spectral statistics of the adjacency matrix of inhomogeneous random graphs across all sparsity regimes, providing explicit covariance formulas under the assumption that the variance…

Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…

We investigate the hyperuniformity of marked Gibbs point processes with weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Some variants of stability and range assumptions are posed on the…

We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Ess\'een bounds in Central Limit Theorems (CLTs) involving multiple Wiener-It\^o integrals with respect to a general…

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,…

We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit…

Gibbs sampling is a common procedure used to fit finite mixture models. However, it is known to be slow to converge when exploring correlated regions of a parameter space and so blocking correlated parameters is sometimes implemented in…

Mesoscopic theory for self-assembling systems near a planar confining surface is developed. Euler- Lagrange (EL) equations and the boundary conditions (BC) for the local volume fraction and the correlation function are derived from the DFT…

We develop a strong coupling approach for a general lattice problem. We argue that this strong coupling perspective represents the natural framework for a generalization of the dynamical mean field theory (DMFT). The main result of this…

We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every…

In this article, we fill a gap in the literature on Hawkes processes. In particular, we derive a CLT for a non linear compound marked Hawkes process. We also provide an upper bound on the convergence rate using the functional 1-Wasserstein…

We generalize the Poisson limit theorem to binary functions of random objects whose law is invariant under the action of an amenable group. Examples include stationary random fields, exchangeable sequences, and exchangeable graphs. A…

Many qualitative observations on the glass transition in classical fluids are well described by the mode coupling theory (MCT) but the extent of the non-ergodicity domain is often over-estimated by this theory. Making it more quantitative…