Related papers: Central Limit Theorem in Disordered Monomer-Dimer …

In this article we establish new central limit theorems for Ruppert-Polyak averaged stochastic gradient descent schemes. Compared to previous work we do not assume that convergence occurs to an isolated attractor but instead allow…

We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the cumulant method.

The statistical scattering properties of wave transport in disordered waveguides are derived perturbatively within the transition matrix formalism. The limiting macroscopic statistic of the wave transport, emerges as a consequence of a…

This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of…

Suppose $B_i:= B(p,r_i)$ are nested balls of radius $r_i$ about a point $p$ in a dynamical system $(T,X,\mu)$. The question of whether $T^i x\in B_i$ infinitely often (i. o.) for $\mu$ a.e.\ $x$ is often called the shrinking target problem.…

We consider a generalization of the so-called divide and color model recently introduced by Haggstrom. We investigate the behaviour of the magnetization in large boxes and its fluctuations. Thus, laws of large numbers and Central Limit…

We show how decimated Gibbs measures which have an unbroken continuous symmetry due to the Mermin-Wagner theorem, although their discrete equivalents have a phase transition, still can become non-Gibbsian. The mechanism rests on the…

We introduce a modified Consensus-Based Optimization model that admits a fully unified and rigorous analysis of its finite-particle dynamics, the associated McKean--Vlasov equation, and their optimization behavior under a single set of…

We consider a Bayesian hierarchical version of the normal theory general linear model which is practically relevant in the sense that it is general enough to have many applications and it is not straightforward to sample directly from the…

We study conditions under which treatment effect estimators constructed under the no-interference assumption in randomized experiments are asymptotically normal in the presence of interference. We prove that the standard Horvitz-Thompson…

In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…

We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case…

We study the asymptotic behaviour of the statistic (des+ides) which assigns to an element w of a finite Coxeter group W the number of descents of w plus the number of descents of its inverse. Our main result is a central limit theorem for…

We study a random partial covering model on the $(d-1)$-dimensional unit sphere, where $N$ spherical caps are placed independently and uniformly at random, each covering a surface fraction of $1/N$. This model provides a continuous…

We consider sub-critical configuration models and show that the central limit theorem for any additive statistic holds when the statistics satisfies a fourth moment assumption, a variance lower bound and the degree sequence of graph…

Consider directed polymers in a random environment on the complete graph of size $N$. This model can be formulated as a product of i.i.d. $N\times N$ random matrices and its large time asymptotics is captured by Lyapunov exponents and the…

The correlation functions of an arbitrary number of boundary monomers in the system of close-packed dimers on the square lattice are computed exactly in the scaling limit. The equivalence of the 2n-point correlation functions with those of…

We study the monomer--dimer partition function on the configuration model of random $d$-regular, $l$-uniform hypergraphs. For fixed $d,l\ge2$, we prove quenched free-energy limits in explicit parameter regimes. The proof combines…

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology…

We consider a general class of spin systems with potentially unbounded real-valued spins, defined via a single-site potential with super-Gaussian tails on general graphs, allowing for both short- and long-range interactions. This class…