Related papers: Random linear systems with sparse solutions -- fin…

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…

This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing…

Many sparse linear discriminant analysis (LDA) methods have been proposed to overcome the major problems of the classic LDA in high-dimensional settings. However, the asymptotic optimality results are limited to the case that there are only…

It is well known that symplectic methods have been rigorously shown to be superior to non-symplectic ones especially in long-time computation, when applied to deterministic Hamiltonian systems. In this paper, we attempt to study the…

We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…

We use a method, inspired by Pohozeav's work, to study asymptotic behaviors of non-variational elliptic systems in dimension n greater than two. The results apply to changing sign solutions.

Correlated with the trend of increasing degrees of freedom in robotic systems is a similar trend of rising interest in Spatio-Temporal systems described by Partial Differential Equations (PDEs) among the robotics and control communities.…

Various natural and engineered systems, from urban traffic flow to the human brain, can be described by large-scale networked dynamical systems. These systems are similar in being comprised of a large number of microscopic subsystems, each…

The work of Gantert, Kim, and Ramanan [Large deviations for random projections of $\ell^p$ balls, Ann. Probab. 45 (6B), 2017] has initiated and inspired a new direction of research in the asymptotic theory of geometric functional analysis.…

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…

We consider a class of dissipative stochastic differential equations (SDE's) with time-periodic coefficients in finite dimension, and the response of time-asymptotic probability measures induced by such SDE's to sufficiently regular, small…

This article investigates the asymptotic distribution of penalized estimators with non-differentiable penalties designed to recover low-dimensional pattern structures. Patterns play a central role in estimation, as they reveal the…

Regularized system identification is the major advance in system identification in the last decade. Although many promising results have been achieved, it is far from complete and there are still many key problems to be solved. One of them…

We consider linear models for stochastic dynamics. To any such model can be associated a network (namely a directed graph) describing which degrees of freedom interact under the dynamics. We tackle the problem of learning such a network…

We prove the support recovery for a general class of linear and nonlinear evolutionary partial differential equation (PDE) identification from a single noisy trajectory using $\ell_1$ regularized Pseudo-Least Squares model~($\ell_1$-PsLS).…

In this work, we study the problem of learning a nonlinear dynamical system by parameterizing its dynamics using basis functions. We assume that disturbances occur at each time step with an arbitrary probability $p$, which models the…

In this paper, we study the precise late-time asymptotic behaviour of small data solutions for the Vlasov-Poisson system in dimension three. First, we show that the spatial density and the force field satisfy asymptotic self-similar…

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

Spatially-coupled LDPC codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially-coupled…

We investigate the large deviation principle (LDP) of the stationary solutions of stochastic functional differential equations (SFDEs) with infinite delay under small random perturbation. First, we demonstrate the existence and uniqueness…