Related papers: Normal Limits, Nonnormal Limits, and the Bootstrap…

We prove the annealed Central Limit Theorem for random walks in bistochastic random environments on $Z^d$ with zero local drift. The proof is based on a "dynamicist's interpretation" of the system, and requires a much weaker condition than…

Given a pair of isolated devices that accept random binary inputs and return binary outputs, a user can deduce from the observed data alone if the underlying mechanism can be explained classically. Bell's theorem further states that a…

We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…

This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable…

An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over the field with two elements. For systems that can…

We show weak convergence of quantile and expectile processes to Gaussian limit processes in the space of bounded functions endowed with an appropriate semimetric which is based on the concepts of epi- and hypo convergence as introduced in…

We establish a necessary and sufficient condition for the quantile process based on iid sampling to converge in distribution in $L^1(0,1)$. The condition is that the quantile function is locally absolutely continuous and satisfies a slight…

We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem,…

We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…

We study the evolution of cosmological domain walls in models with asymmetric potentials. Our research goes beyond the standard case of spontaneous breaking of an approximate symmetry. When the symmetry is explicitly broken the potential…

The bootstrap is a popular method of constructing confidence intervals due to its ease of use and broad applicability. Theoretical properties of bootstrap procedures have been established in a variety of settings. However, there is limited…

We study the disordered quantum walk in one dimension, and obtain the weak limit theorem.

We completely characterize the weak differentiability (or, in other words Gateaux differentiability) of the norm in the spaces of bounded multilinear maps. Also, we obtain a multilinear generalization of the well-known Bhatia-\v{S}emrl…

A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample…

In this paper we show that the limiting distribution of the real and the imaginary part of the double Fourier transform of a stationary random field is almost surely an independent vector with Gaussian marginal distributions, whose variance…

We prove annealed central limit theorems for finite pattern counts in the measurement record of discrete-time quantum trajectories generated by repeated measurements in a disordered environment. Under summable mixing assumptions on the…

Let $\{X_n, n \ge 1\}$ be a sequence of stationary associated random variables. We discuss another set of conditions under which a central limit theorem for U-statistics based on $\{X_n, n \ge 1\}$ holds. We look at U-statistics based on…

In this paper we develop a novel bootstrap test for the comparison of two multinomial distributions. The two distributions are called {\it equivalent} or {\it similar} if a norm of the difference between the class probabilities is smaller…

We prove a Functional Central Limit Theorem for the position of a Tagged Particle in the one-dimensional Asymmetric Simple Exclusion Process in the hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle…

Quantum correlations, like entanglement, represent the characteristic trait of quantum mechanics, and pose essential issues and challenges to the interpretation of this pillar of modern physics. Although quantum correlations are largely…