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We show that the delta function potential can be exploited along with perturbation theory to yield the result of certain infinite series. The idea is that any exactly soluble potential if coupled with a delta function potential remains…
This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…
We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter Delta is varied spin transport changes from ballistic…
In this paper, we propose a data based transformation for infinite-dimensional Gaussian processes and derive its limit theorem. For a classification problem, this transformation induces complete separation among the associated Gaussian…
In work of C. A. Tracy and the author asymptotic formulas were derived for certain operator determinants which gave solutions to the cylindrical Toda equations. Later the author considered a more general class of operators which retained…
Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly…
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…
Recent work has suggested that in highly correlated systems, such as sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity…
A variational formulation is introduced for the Oseen equations written in terms of vor\-ti\-city and Bernoulli pressure. The velocity is fully decoupled using the momentum balance equation, and it is later recovered by a post-process. A…
The science of cause and effect is extremely sophisticated and extremely hard to scale. Using a controlled experiment, scientists get rich insights by analyzing global effects, effects in different segments, and trends in effects over time.…
Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy…
Analysis of experimental data must sometimes deal with abrupt changes in the distribution of measured values. Setting upper limits on signals usually involves a veto procedure that excludes data not described by an assumed statistical…
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…
The macroscale structure and microscale fluctuation statistics of late-time asymptotic steady state flows in cylindrical geometries is studied using the methods of equilibrium statistical mechanics. The axisymmetric assumption permits an…
Polarization phenomena are essential for the understanding of elementary processes, and are typically large in the threshold region. The selection rules with respect to P-parity, angular momentum, isotopic spin and the Pauli principle allow…
Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…
In causal inference, a fundamental task is to estimate the effect resulting from a specific treatment, which is often handled with inverse probability weighting. Despite an abundance of attention to the advancement of this task, most…
Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
The resonance $\Delta(1232)$ with spin-parity ${3 \over 2}^+$, which contributes dominantly to the reactions like $\gamma N \to \pi N$ and $NN \to NN\pi$ at intermediate energies, may be expected to be produced in characteristically…