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This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery…
We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…
A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of…
We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The…
We derive an asymptotic formula for operator product expansion coefficients of heavy operators in two dimensional conformal field theory. This follows from modular invariance of the genus two partition function, and generalises the…
A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion…
In this paper, we propose improved estimation method for logistic regression based on subsamples taken according the optimal subsampling probabilities developed in Wang et al. 2018 Both asymptotic results and numerical results show that the…
In this paper, insight is given in the techniques used to compute asymptotic expansions. In a broad fashion the technique is described. Most of the results apply to the paper "An expansion for the maximum likelihood estimator and its…
We conclude our work [arXiv:2403.07628, arXiv:2503.12644] on asymptotic expansions at the soft edge for the classical $n$-dimensional Gaussian and Laguerre ensembles, now studying the gap-probability generating functions. We show that the…
In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. New integral representations for the remainder terms of these asymptotic expansions are found…
We establish asymptotic expansions for factorial moments of following distributions: number of cycles in a random permutation, number of inversions in a random permutation, and number of comparisons used by the randomized quick sort…
We continue our work [arXiv:2403.07628] on asymptotic expansions at the soft edge for the classical $n$-dimensional Gaussian and Laguerre random matrix ensembles. By revisiting the construction of the associated skew-orthogonal polynomials…
I study the product of independent identically distributed $D\times D$ random probability matrices. Some exact asymptotic results are obtained. I find that both the left and the right products approach exponentially to a probability…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
We present a differential formulation of the recursion formula of the hierarchical model which provides a recursive method of calculation for the high-temperature expansion. We calculate the first 30 coefficients of the high temperature…
In a previous paper an asymptotic expansion for lambda_d in powers of 1/d was developed. The results of computer computations for some terms in the expansion, as well as various quantities associated to the expansion, are herein presented.…
This article studies some numerical approximations of the homogenized matrix for stochastic linear elliptic partial differential equations in divergence form. We focus on the case when the underlying random field is a small perturbation of…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
An assumed density approximate likelihood is derived for a class of partially observed stochastic compartmental models which permit observational over-dispersion. This is achieved by treating time-varying reporting probabilities as latent…