Related papers: A minimalist version of the circle method and Diop…

In this paper, we present an improved continued fraction approximation of the Wallis ratio. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the double-side inequality related to…

Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…

We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…

Walk on Spheres algorithms leverage properties of Brownian Motion to create Monte Carlo estimates of solutions to a class of elliptic partial differential equations. We propose a new caching strategy which leverages the continuity of paths…

The purpose of this note is to study the existence of a nontrivial solution for an elliptic system which comes from a newly introduced mathematical problem so called Field-Road model. Specifically, it consists of coupled equations set in…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

We study the number of representations of an integer n=F(x_1,...,x_s) by a homogeneous form in sufficiently many variables. This is a classical problem in number theory to which the circle method has been succesfully applied to give an…

It is shown that the non-homogeneous Dirichlet and Neuman problems for the $2^{nd}$-order Seiberg-Witten equation admit a regular solution once the $\mathcal{H}$-condition (described in the article) is satisfied. The approach consist in…

We study the arithmetic analogue of maximal functions on diagonal hypersurfaces. This paper is a natural step following the papers of \cite{Magyar_dyadic}, \cite{Magyar_ergodic} and \cite{MSW}. We combine more precise knowledge of…

Variational inference is a general framework to obtain approximations to the posterior distribution in a Bayesian context. In essence, variational inference entails an optimization over a given family of probability distributions to choose…

In this paper, we study a density version of Waring's problem. We prove that a positive density subset of $k$th-powers forms an asymptotic additive basis of order $O(k^2)$ provided that the relative lower density of the set is greater than…

In this paper we prove the existence of asymptotic moments, and an estimate on the tails of the limiting distribution, for a specific class of almost periodic functions. Then we introduce the hyperbolic circle problem, proving an estimate…

It is classically known that the circle method produces an asymptotic for the number of representations of a tuple of integers $(n_1,\ldots,n_R)$ by a system of quadratic forms $Q_1,\ldots, Q_R$ in $k$ variables, as long as $k$ is…

We present a new and relatively elementary method for studying the solution of the initial-value problem for dispersive linear and integrable equations in the large-$t$ limit, based on a generalization of steepest descent techniques for…

Asymptotic results are derived for the number of random walks in alcoves of affine Weyl groups (which are certain regions in $n$-dimensional Euclidean space bounded by hyperplanes), thus solving problems posed by Grabiner [J. Combin. Theory…

For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…

We prove the Central Limit Theorem and superpolynomial mixing for environment viewed for the particle process in quasi periodic Diophantine random environment. The main ingredients are smoothness estimates for the solution of the Poisson…

Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…

We describe an approach to improving model fitting and model generalization that considers the entropy of distributions of modelling residuals. We use simple simulations to demonstrate the observational signatures of overfitting on ordered…

We studied the asymptotic behavior of local solutions for strongly coupled critical elliptic systems near an isolated singularity. For the dimension less than or equal to five we prove that any singular solution is asymptotic to a…