Related papers: Accurate analytical approximation formulae for lar…
Continuous determinantal point processes (DPPs) are a class of repulsive point processes on $\mathbb{R}^d$ with many statistical applications. Although an explicit expression of their density is known, it is too complicated to be used…
Based on the negative binomial model for the duration of wet periods measured in days, an asymptotic approximation is proposed for the distribution of the maximum daily precipitation volume within a wet period. This approximation has the…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
This research proposes a new method for approximating the solution of the inverse problem of finding a rational function that generates known local dynamics within distinct, disjoint closed balls in non-Archimedean fields. Although our…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
Rainfall is an important component of the climate system and its statistical properties are vital for prediction purposes. In this study, we have developed a statistical method for constructing the distribution of annual precipitation. The…
We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…
We provide exact asymptotic expressions for the performance of regression by an $L-$layer deep random feature (RF) model, where the input is mapped through multiple random embedding and non-linear activation functions. For this purpose, we…
Data assimilation plays a crucial role in modern weather prediction, providing a systematic way to incorporate observational data into complex dynamical models. The paper addresses continuous data assimilation for a model arising as a…
We study large deviations asymptotics for a class of unbounded additive functionals, interpreted as normalized accumulated areas, of one-dimensional Langevin diffusions with sub-linear gradient drifts. Our results provide parametric…
Using a generalisation of the detailed balance for systems maintained out of equilibrium by contact with 2 reservoirs at unequal temperatures or at unequal densities, we recover the fluctuation theorem for the large deviation funtion of the…
We highlight the current state-of-the-art in modeling emulsion rheology, ranging from dilute to jammed dense systems. We focus on analytical and numerical methods developed for calculating, computing, and tracking drop deformation en route…
We describe a simple form of importance sampling designed to bound and compute large-deviation rate functions for time-extensive dynamical observables in continuous-time Markov chains. We start with a model, defined by a set of rates, and a…
The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the…
The prediction of the drop size distribution (DSD) resulting from liquid atomization is key to the optimization of multi-phase flows, from gas-turbine propulsion, through agriculture, to healthcare. Obtaining high-fidelity data of liquid…
Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance…
We derive rigorously from the water waves equations new irrotational shallow water models for the propagation of surface waves in the case of uneven topography in horizontal dimensions one and two. The systems are made to capture the…
The saddlepoint approximation gives an approximation to the density of a random variable in terms of its moment generating function. When the underlying random variable is itself the sum of $n$ unobserved i.i.d. terms, the basic classical…
The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in non-relativistic conformal field theory is obtained. This field is used to compute Schr\"odinger-invariant n-point…