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A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…
In this paper we study the asymptotic behavior of solutions for a non-local non-autonomous scalar quasilinear parabolic problem in one space dimension. Our aim is to give a fairly complete description of the the forwards asymptotic behavior…
We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…
Symbolic models have recently spurred the interest of the research community because they offer a correct-by-design approach to the control of embedded and cyber-physical systems. In this paper we address construction of symbolic models for…
We establish non-asymptotic error bounds for the classical Maximal Likelihood Estimation of the transition matrix of a given Markov chain. Meanwhile, in the reversible case, we propose a new reversibility-preserving online Symmetric…
We investigate the fractional diffusion approximation of a kinetic equation set in a bounded interval with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion…
We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations,…
The fits of 0.4 Ca(NO_3)_2 0.6 K(NO_3) (CKN) by schematic mode-coupling models [V. Krakoviack and C. Alba-Simionesco, J. Chem. Phys. 117, 2161-2171 (2002)] are analyzed by asymptotic expansions. The validity of both the power-law and the…
There has been remarkable progress over the past decade in establishing finite-sample, non-asymptotic bounds on recovering unknown system parameters from observed system behavior. Surprisingly, however, we show that the current…
We study the matrix discrepancy problem in the average-case setting. Given a sequence of $m \times m$ symmetric matrices $A_1,\ldots,A_n$, its discrepancy is defined as the minimal spectral norm over all signed sums $\sum_{i=1}^n x_iA_i$…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
In this article, we give a unified theory for constructing boundary layer expansions for dis-cretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit a natural assumption on the discretization under which the…
We investigate the asymptotic risk of a general class of overparameterized likelihood models, including deep models. The recent empirical success of large-scale models has motivated several theoretical studies to investigate a scenario…
We probabilistically bound the error of a solution to a radial network topology learning problem where both connectivity and line parameters are estimated. In our model, data errors are introduced by the precision of the sensors, i.e.,…
Accuracy of a relativistic weak-coupling expansion procedure for solving the Hamiltonian bound-state eigenvalue problem in theories with asymptotic freedom is measured using a well-known matrix model. The model is exactly soluble and simple…
We investigate the asymptotic behavior of high-codimensional area-minimizing locally rectifiable currents in hyperbolic space, addressing a problem posed by F.H. Lin and establishing ``boundary regularity at infinity" results for such…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…