Related papers: Reduction principle for functionals of strong-weak…

We deal with the problem of asymptotic distribution of first return times to shrinking balls under iteration generated by a large general class of dynamical systems called weakly Markov. Our ultimate main result is that these distributions…

We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…

The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the…

Spin (spherical) random fields are very important in many physical applications, in particular they play a key role in Cosmology, especially in connection with the analysis of the Cosmic Microwave Background radiation. These objects can be…

We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…

We support and generalize a weak selection rule predicted recently for the self-similar asymptotics of the distribution function (DF) in the zero-volume-fraction limit of Ostwald ripening (OR). An asymptotic perturbation theory is developed…

Let $G$ be a directed graph on finitely many vertices and edges, and assign a positive weight to each edge on $G$. Fix vertices $u$ and $v$ and consider the set of paths that start at $u$ and end at $v$, self-intersecting in any number of…

This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish…

Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the results for continuous-time settings have…

This article is a review of functional $f(R)$ approximations in the asymptotic safety approach to quantum gravity. It mostly focusses on a formulation that uses a non-adaptive cutoff, resulting in a second order differential equation. This…

The classical theory of rank-based inference is entirely based either on ordinary ranks, which do not allow for considering location (intercept) parameters, or on signed ranks, which require an assumption of symmetry. If the median, in the…

In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…

We study the asymptotic behavior of random time changes of dynamical systems. As random time changes we propose three classes which exhibits different patterns of asymptotic decays. The subordination principle may be applied to study the…

In this paper, we derive high-dimensional asymptotic properties of the Moore-Penrose inverse and, as a byproduct, of various ridge-type inverses of the sample covariance matrix. In particular, the analytical expressions of the asymptotic…

For $\nu\in[0,1]$ and a complex parameter $\sigma,$ $Re\, \sigma>0,$ we discuss a linear inhomogeneous functional difference equation with variable coefficients on a complex plane $z\in\mathbb{C}$: \[…

Studying Birkhoff sums of non-integrable functions involves the challenge of large observations depending on the sampled orbit, which prevents pointwise limit theorems. To address this issue, the largest observations are removed, this…

We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labelled trees with given…

Deep learning models, such as wide neural networks, can be conceptualized as nonlinear dynamical physical systems characterized by a multitude of interacting degrees of freedom. Such systems in the infinite limit, tend to exhibit simplified…

Likelihood-free inference for simulator-based statistical models has recently attracted a surge of interest, both in the machine learning and statistics communities. The primary focus of these research fields has been to approximate the…

Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…