相关论文: Central limit theorem for the solution of the Kac …

We prove an almost sure weak limit theorem for simple linear rank statistics for samples with continuous distributions functions. As a corollary the result extends to samples with ties, and the vector version of an a.s. central limit…

We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number…

The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almost everywhere (provided the entropy is…

Various quantum analogues of the central limit theorem, which is one of the cornerstones of probability theory, are known in the literature. One such analogue, due to Cushen and Hudson, is of particular relevance for quantum optics. It…

We provide new bounds for the rate of convergence of the multivariate Central Limit Theorem in Wasserstein distances of order $p \geq 2$. In particular, we obtain what we conjecture to be the asymptotically optimal rate whenever the density…

We consider a mean-field control problem in which admissible controls are required to be adapted to the common noise filtration. The main objective is to show how the mean-field control problem can be approximates by time consistent…

We derive two estimates for the deviation of the $N$-particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Particular care is paid to the long-time properties of our…

We give a central limit theorem, which has applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced generalized Polya urns.

In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…

We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

Using Stein's method, we prove an abstract result that yields multivariate central limit theorems with a rate of convergence for time-dependent dynamical systems. As examples we study a model of expanding circle maps and a quasistatic…

The Kac model is a simplified model of an $N$-particle system in which the collisions of a real particle system are modeled by random jumps of pairs of particle velocities. Kac proved propagation of chaos for this model, and hence provided…

We study a model of random colliding particles interacting with an infinite reservoir at fixed temperature and chemical potential. Interaction between the particles is modeled via a Kac master equation \cite{kac}. Moreover, particles can…

In the seventies, Charles Stein revolutionized the way of proving the Central Limit Theorem by introducing a method that utilizes a characterization equation for Gaussian distribution. In the last 50 years, much research has been done to…

We prove entropic and total variation versions of the Erd\H{o}s-Kac limit theorem for the maximum of the partial sums of i.i.d. random variables with densities.

We investigate Maxwell's attempt to justify the mathematical assumptions behind his 1860 Proposition IV according to which the velocity components of colliding particles follow the normal distribution. Contrary to the commonly held view we…

We consider a system of $M$ particles in contact with a heat reservoir of $N\gg M$ particles. The evolution in the system and the reservoir, together with their interaction, are modeled via the Kac's Master Equation. We chose the initial…

We discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space - discrete time version of this model and, under suitable scaling, we show its functional…

We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein-Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function…