Related papers: Central limit theorem for the stratified resamplin…
This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous…
In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…
We establish a central limit theorem (CLT) for families of products of $\epsilon$-independent random variables. We utilize graphon limits to encode the evolution of independence and characterize the limiting distribution. Our framework…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
We establish the central limit theorem for the number of groups at the equilibrium of a coagulation-fragmentation process given by a parameter function with polynomial rate of growth. The result obtained is compared with the one for random…
In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling…
The general model of coagulation is considered. For basic classes of unbounded coagulation kernels the central limit theorem (CLT) is obtained for the fluctuations around the dynamic law of large numbers (LLN). A rather precise rate of…
In this paper, we study a simple model of a diffusive particle on a line, undergoing a stochastic resetting with rate $r$, via rescaling its current position by a factor $a$, which can be either positive or negative. For $|a|<1$, the…
A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This ``Stochastic Renormalization Group'' (SRG) expresses statistical…
The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…
A novel strategy that combines a given collection of $\pi$-reversible Markov kernels is proposed. At each Markov transition, one of the available kernels is selected via a state-dependent probability distribution. In contrast to random-scan…
We consider deterministic random walks on the real line driven by irrational rotations, or equivalently, skew product extensions of a rotation by $\alpha$ where the skewing cocycle is a piecewise constant mean zero function with a jump by…
This work focuses on the convergence analysis of adaptive distributed beamforming schemes that can be reformulated as local random search algorithms via a random search framework. Once reformulated as local random search algorithms, it is…
We report a detailed and systematic study of wave propagation through a stochastic absorbing random medium. Stochastic absorption is modeled by introducing an attenuation constant per unit length $\alpha$ in the free propagation region of…
We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions…
A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated…
In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…
We show how a central limit theorem for Poisson model random polygons implies a central limit theorem for uniform model random polygons. To prove this implication, it suffices to show that in the two models, the variables in question have…
The aggregation of particles in the free molecular regime is determined approximately for situations with a high degree of translational energy equilibration. The mean particle sizes develop linearly in time. Scaling relations are used to…
We propose a homotopy sampling procedure, loosely based on importance sampling. Starting from a known probability distribution, the homotopy procedure generates the unknown normalization of a target distribution. In the context of…