Related papers: Comment on ``Proposed central limit behavior in de…
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…
We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling…
The classic central limit theorem and $\alpha$-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the…
Simulations are made of a probe particle diffusing through a complex fluid. Probe particle motions are described by the Mori-Zwanzig equation and Mori's orthogonal hierarchy of random forces scheme, subject to the approximation that the…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
We extend our recent result [Cipolloni, Erd\H{o}s, Schr\"oder 2019] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices $X$ with independent, identically distributed complex entries to the real…
An obvious way to simulate a L\'evy process $X$ is to sample its increments over time $1/n$, thus constructing an approximating random walk $X^{(n)}$. This paper considers the error of such approximation after the two-sided reflection map…
We focus on the FeigenbaumCoulletTresser point of the dissipative one-dimensional z logistic map. We show that sums of iterates converge to q Gaussian distributions, which optimize the nonadditive entropic functional Sq under simple…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal…
We investigate the asymptotic behavior of Bayesian posterior distributions under independent and identically distributed ($i.i.d.$) misspecified models. More specifically, we study the concentration of the posterior distribution on…
In this paper, we study some aspects on random analysis on the L\'eevy stochastic processes with margins following generalized hyperbolic distributions generated by gamma laws. In particular we study the boundedness of its total variations…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices,…
This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…
The Rosenfeld functional provides excellent results for the prediction of the fluid phase of hard convex particle systems but fails beyond the freezing point. The reason for this limitation is the neglect of orientational and distance…
Critiques presented by P. Grassberger in Phys. Rev. Lett. 95, 140601 (2005) are addressed.
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…
One reason for the well known fact that the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit has been identified long ago: it is insufficient decay of the probability density either near infinity or…
\cite{tsagris2025a} proposed the generalized circular projected Cauchy (GCPC) distribution, whose special case is the wrapped Cauchy distribution. In this paper we first derive the relationship with the wrapped Cauchy distribution, and then…