Related papers: Calculation and Estimation of the Poisson kernel

We establish formulas for the constant factor in several asymptotic estimates related to the distribution of integer and polynomial divisors. The formulas are then used to approximate these factors numerically.

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…

In Random Matrix Theory the local correlations of the Laguerre and Jacobi Unitary Ensemble in the hard edge scaling limit can be described in terms of the Bessel kernel (containing a parameter $\alpha$). In particular, the so-called hard…

This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…

We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.

In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size.…

We provide short-time asymptotics with rates of convergence for the Laplace Dirichlet heat kernel in a ball. The boundary behaviour is precisely described. Presented results may be considered as a complement or a generalization of the…

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…

The plane partition polynomial $Q_n(x)$ is the polynomial of degree $n$ whose coefficients count the number of plane partitions of $n$ indexed by their trace. Extending classical work of E.M. Wright, we develop the asymptotics of these…

We give a bound, linear in the complexity of the surface, on the asymptotic dimension of the curve complex as well as the capacity dimension of the ending lamination space.

We obtain nontrivial estimates of quadratic character sums of division polynomials $\Psi_n(P)$, $n=1,2, ...$, evaluated at a given point $P$ on an elliptic curve over a finite field of $q$ elements. Our bounds are nontrivial if the order of…

The quantization of gauge fields and gravitation on manifolds with boundary makes it necessary to study boundary conditions which involve both normal and tangential derivatives of the quantized field. The resulting one-loop divergences can…

We consider the problem of simultaneously inferring the heterogeneous coefficient field for a Robin boundary condition on an inaccessible part of the boundary along with the shape of the boundary for the Poisson problem. Such a problem…

We deduce the non-asymptotical bilateral estimates for moment inequalities for sums of non-negative independent random variables, based on the correspondent estimates for the so-called Bell functions and the Poisson distribution.

We derive the local and central limit theorems for the Stirling numbers of the second kind by elementary means, obtaining as corollaries effective asymptotic estimates for the Bell numbers and for the moments of the distribution. We also…

We consider the exterior free boundary Bernoulli problem in the case of a rough given domain. An asymptotic analysis shows that the solution of the initial problem can be approximated by the solution of a non-rough Bernoulli problem at…

We provide a rather general and very simple to compute lower bound for the asymptotic convergence factor of compact subsets of the set of complex numbers with connected complement and finitely many connected components .

We study a local thinning $T_r$ that retains a point with probability $p(n_r)$, where $n_r$ counts neighbors within radius $r$. For Poisson input with spatially varying intensity, we obtain an exact intensity via a Poisson--mixture formula…

For the finite element solution of Poisson's equation, a local a posteriori error estimation based on the Hypercircle method is proposed. Even for the solution of Poisson's equation without the $H^2$ regularity, this method can provide…

For the standard symplectic forms on Jacobi and CMV matrices, we compute Poisson brackets of OPRL and OPUC, and relate these to other basic Poisson brackets and to Jacobians of basic changes of variable.