Related papers: Strategies for Asymptotic Normalization
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…
Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation…
New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential…
For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this paper, we release the degree sequences of the binary networks…
Standard techniques for treating linear recurrences no longer apply for quadratic recurrences. It is not hard to determine asymptotics for a specific parametrized model over a wide domain of values (all $p \neq 1/2$ here). The gap between…
We investigate the performance of parallel and adaptive quantum channel discrimination strategies for a finite number of channel uses. It has recently been shown that, in the asymmetric setting with asymptotically vanishing type I error…
Singularly-perturbed ordinary differential equations often exhibit Stokes' phenomenon, which describes the appearance and disappearance of oscillating exponentially small terms across curves in the complex plane known as Stokes curves.…
We give sufficient conditions for the asymptotic normality of linear combinations of order statistics (L-statistics) in the case of simple random samples without replacement. In the first case, restrictions are imposed on the weights of…
In a recent work, a central limit theorem for pattern counts in random planar maps was proven by reducing the problem to a face count problem. We provide a shorter proof by circumventing this reduction through the computation of bivariate…
Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the SAFE method and include only the first non-zero wave-related correction to the familiar…
An asymmetric variant of the contact process where the activity spreads with different and independent random rates to the left and to the right is introduced. A real space renormalization scheme is formulated for model by means of which it…
We introduce a concept of asymptotic principal values which enables us to handle rigorously singular integrals of higher-order poles encountered in the computation of various quantities based on correlation functions of a vacuum. Several…
We consider a recurrent random walk of i.i.d. increments on the one-dimensional integer lattice and obtain a formula relating the hitting distribution of a half-line with the potential function, $a(x)$, of the random walk. Applying it, we…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
There is a wide literature on change point tests, but the case of variables with infinite variances is essentially unexplored. In this paper we address this problem by studying the asymptotic behavior of trimmed CUSUM statistics. We show…
We study an extension of Plotkin's call-by-value lambda-calculus via two commutation rules (sigma-reductions). These commutation rules are sufficient to remove harmful call-by-value normal forms from the calculus, so that it enjoys elegant…
In this paper, we introduce a new class of optimization problems whose objective functions are weakly homogeneous relative to the constraint sets. By using the normalization argument in asymptotic analysis, we prove two criteria for the…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have…
The aim of the paper is to study the limit distributions and the asymptotic behavior of summation arithmetic functions. A probabilistic approach based on the use of the axioms of probability theory is used for these purposes. Sufficient…