Related papers: The realization problem for tail correlation funct…
The application of the consolidation equation is based on Taylor's approximate solution alone. The existence of the exact solution emerged from the analysis of the logical structure of d'Alambert's, Fourier' and Laplace's differential…
We study sampling from a target distribution ${\nu_* = e^{-f}}$ using the unadjusted Langevin Monte Carlo (LMC) algorithm. For any potential function $f$ whose tails behave like ${\|x\|^\alpha}$ for ${\alpha \in [1,2]}$, and has…
Given two multivariate copulas with corresponding tail dependence functions, we investigate the relation between a natural tail dependence ordering $\leq_{tdo}$ and the order $\leq_{loc}$ of local stochastic dominance. We show that,…
The long-time behavior of the velocity autocorrelation function (VACF) is investigated by the molecular dynamics simulation of a two-dimensional system which has both a many-body interaction and a random potential. With strengthening the…
This paper studies the supremum of a chi-square process with trend over a threshold-dependent-time horizon. Under the assumption that the chi-square process is generated from a centered self-similar Gaussian process and the trend function…
A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities: (i) The optimal terminal wealth $X^*(T) : = X_{\varphi^*}(T)$ of the problem to maximize the expected $U$-utility…
The T product operation between two three order tensors was invented around 2011 and it arises from many applications, such as signal processing, image feature extraction, machine learning, computer vision, and the multiview clustering…
A trace ratio optimization problem over the Stiefel manifold is investigated from the perspectives of both theory and numerical computations. At least three special cases of the problem have arisen from Fisher linear discriminant analysis,…
We study multivariate tail-dependence compatibility for complete and partial signed tail families, treating lower-tail, upper-tail, and mixed configurations in one geometric witness representation indexed by active coordinate sets and sign…
It is investigated necessary and sufficient conditions on topological spaces $X=\prod\limits _{s\in S}X_s$ and $Y=\prod\limits _{t\in T}Y_t$ for the dependence of every separately continuous functions $f:X\times Y\to \mathbb R$ on at most…
Density Functional Theory (DFT) is used extensively in the computation of electronic properties of matter, with various applications. Approximating the exchange-correlation (XC) functional is the key to the Kohn-Sham DFT approach, the basis…
We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$,…
Slow mixing is the central hurdle when working with Markov chains, especially those used for Monte Carlo approximations (MCMC). In many applications, it is only of interest to estimate the stationary expectations of a small set of…
We propose a multi-boundary generalization of thermofield double states (TFD) of a two-dimensional conformal field theory (CFT) and show, through a conformal map to the complex plane, that they are closely related to multi-point correlation…
We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a…
We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…
Percolation has two mean-field theories, the Gaussian fixed point (GFP) and the Landau mean-field theory or the complete graph (CG) asymptotics. By large-scale Monte Carlo simulations, we systematically study the interplay of the GFP and CG…
Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…
The paper presents an efficient method for simulating the tails of a target variable Z=h(X) which depends on a set of basic variables X=(X_1, ..., X_n). To this aim, variables X_i, i=1, ..., n are sequentially simulated in such a manner…
In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…