相关论文: Randomization and the Gross-Pitaevskii hierarchy

What is the connection of random matrices with integrable systems? Is this connection really useful? The answer to these questions leads to a new and unifying approach to the theory of random matrices. Introducing an appropriate time…

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…

Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on the domain is an example of such an operator. The estimates…

In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…

Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…

We study the stochastic $p$-Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linear convergence in space and $1/2$ convergence in time.…

In this work, we study the Gross-Pitaevskii hierarchy on general --rational and irrational-- rectangular tori of dimension two and three. This is a system of infinitely many linear partial differential equations which arises in the rigorous…

While phases and phase transitions are conventionally described by local order parameters in real space, we present a unified framework characterizing the phase transition through the geometry of configuration space defined by the…

We consider the large-scale regularity of solutions to second-order linear elliptic equations with random coefficient fields. In contrast to previous works on regularity theory for random elliptic operators, our interest is in the…

Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Approximate operators, learned from data, can serve as efficient…

Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…

We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fej\'er monotone sequences in a broad metric context. Concretely, our result explicitly constructs a rate of convergence for such process, both in mean…

We consider the computation of an approximately stationary point for a Lipschitz and semialgebraic function $f$ with a local oracle. If $f$ is smooth, simple deterministic methods have dimension-free finite oracle complexities. For the…

We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…

We prove an exact fourth moment bound for the normal approximation of random variables belonging to the Wiener chaos of a general Poisson random measure. Such a result -- that has been elusive for several years -- shows that the so-called…

A variety of problems in distributed control involve a networked system of autonomous agents cooperating to carry out some complex task in a decentralized fashion, e.g., orienting a flock of drones, or aggregating data from a network of…

Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…

Randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome-generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. R. A.…

In this work, we investigate the generalization properties of random feature methods. Our analysis extends prior results for Tikhonov regularization to a broad class of spectral regularization techniques and further generalizes the setting…

We propose a Lawson-time-splitting extended Fourier pseudospectral (LTSeFP) method for the numerical integration of the Gross-Pitaevskii equation with time-dependent potential that is of low regularity in space. For the spatial…