相关论文: Four moments theorems on Markov chaos

Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…

The generalised random graph contains $n$ vertices with positive i.i.d. weights. The probability of adding an edge between two vertices is increasing in their weights. We require the weight distribution to have finite second moments and…

Adapting the spectral viewpoint suggested in Ledoux (2012) in the context of symmetric Markov diffusion generators and recently exploited in the non-diffusive setup of a Poisson random measure by D\"obler and Peccati (2017), we investigate…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces…

Motivated by the problem of computing the distribution of the largest distance $d_{\max}$ between $n$ random points on a circle we derive an explicit formula for the moments of the maximal component of a random vector following a Dirichlet…

We treat the probability distributions for quadratic quantum fields, averaged with a Lorentzian test function, in four-dimensional Minkowski vacuum. These distributions share some properties with previous results in two-dimensional…

Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…

Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…

We prove that a random distribution in two dimensions which is conformally invariant and satisfies a natural domain Markov property is a multiple of the Gaussian free field. This result holds subject only to a fourth moment assumption.

In this article, we give explicit bounds on the Wasserstein and the Kolmogorov distances between random variables lying in the first chaos of the Poisson space and the standard Normal distribution, using the results proved by Last, Peccati…

We study a Markov process with two components: the first component evolves according to one of finitely many underlying Markovian dynamics, with a choice of dynamics that changes at the jump times of the second component. The second…

Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…

Networks of caustics can occur in the distribution of particles suspended in a randomly moving gas. These can facilitate coagulation of particles by bringing them into close proximity, even in cases where the trajectories do not coalesce.…

The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…

Let $f$ be a Gaussian random field on $\mathbb{R}^d$ and let $X$ be the number of critical points of $f$ contained in a compact subset. A long-standing conjecture is that, under mild regularity and non-degeneracy conditions on $f$, the…

In a seminal paper of 2005, Nualart and Peccati discovered a surprising central limit theorem (called the "Fourth Moment Theorem" in the sequel) for sequences of multiple stochastic integrals of a fixed order: in this context, convergence…

This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…

Theoretical results for importance sampling rely on the existence of certain moments of the importance weights, which are the ratios between the proposal and target densities. In particular, a finite variance ensures square root convergence…

Consider $N$ balls initially placed in $L$ bins. At each time step take a ball from each non-empty bin and \emph{randomly} reassign the balls into the bins.We call this finite Markov chain \emph{General Repeated Balls into Bins} process. It…