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The existence of measure preserving invertible transformations $T$ with simple spectrum is established possessing the following rate of correlation decay $(f(T^k x), f(x)) = O(|k|^{-1/2+{\epsilon}})$ for a dense family of functions $f$ and…
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…
We derive the second-order sampling properties of certain autocovariance and autocorrelation estimators for sequences of independent and identically distributed samples. Specifically, the estimators we consider are the classic lag windowed…
A model-independent method of studying the forward-backward correlations in symmetric high energy processes is developed. The method allows a systematic study of properties of various particle sources and to uncover asymmetric structures…
We use an optical cavity in the regime of intermediate coupling between atom and cavity mode to detect single moving atoms. Degenerate polarization modes allow excitation of the atoms in one mode and collection of spontaneous emission in…
We present a general method to detect nonclassical radiation fields with systems of on-off detectors. We especially study higher order correlations for the identification of nonclassical radiation. This allows us to directly characterize…
Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries,…
In this paper we propose and study a class of nonparametric, yet interpretable measures of association between two random vectors $X$ and $Y$ taking values in $\mathbb{R}^{d_1}$ and $\mathbb{R}^{d_2}$ respectively ($d_1, d_2\ge 1$). These…
A hyperscaling relation for the critical exponents of absorbing phase transitions is tested in the bosonic pair contact process with diffusion. To this end spreading is considered, i.e. the time evolution out of an initial seed. It is shown…
We show how the newly developed method of Periodic Unfolding on Riemannian manifolds can be applied to PDE problems: We consider the homogenization of an elliptic model problem. In the limit, we obtain a generalization of the well-known…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
We study a class of self-repelling diffusions on compact Riemannian manifolds whose drift is the gradient of a potential accumulated along their trajectory. When the interaction potential admits a suitable spectral decomposition, the…
We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent…
Anomaly detection on the attributed network has recently received increasing attention in many research fields, such as cybernetic anomaly detection and financial fraud detection. With the wide application of deep learning on graph…
We discuss the two-dimensional isotropic antiferromagnet in the framework of gauge invariance. Gauge invariance is one of the most subtle useful concepts in theoretical physics, since it allows one to describe the time evolution of complex…
In the uniformly hyperbolic setting it is well known that the set of all measures supported on periodic orbits is dense in the convex space of all invariant measures. In this paper we consider the converse question, in the non-uniformly…
Nuclear mass autocorrelations are investigated as a function of the number of nucleons. The fluctuating part of these autocorrelations is modeled by a parameter free model in which the nucleons are confined in a rigid sphere. Explicit…
We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible…
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…