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Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
We consider the Gaussian approximation for functionals of a Poisson process that are expressible as sums of region-stabilizing (determined by the points of the process within some specified regions) score functions and provide a bound on…
Two-dimensional systems are realized experimentally as thin layers on a substrate. The substrate can have some imperfections (defects of the crystalline structure, chemical impurities, etc.), which demonstrate stronger interaction with the…
Many problems arising in control require the determination of a mathematical model of the application. This has often to be performed starting from input-output data, leading to a task known as system identification in the engineering…
We perform variational studies of the interaction-localization problem to describe the interaction-induced renormalizations of the effective (screened) random potential seen by quasiparticles. Here we present results of careful finite-size…
We study the estimation precision attainable by entanglement-enhanced Ramsey interferometry in the presence of spatiotemporally correlated non-classical noise. Our analysis relies on an exact expression of the reduced density matrix of the…
We study the mild Skorohod solution to the following fractional stochastic heat equation on $\mathbb{R}$: \begin{equation} \begin{cases} \partial_t u(t,x)=-(-\Delta)^{\rho/2} u(t,x) +\beta u(t,x)\delta_0(x)\xi(t),\\ u(0,\cdot)=u_0(x),…
We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(.) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form…
Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…
This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…
Configurational entropy has been revealed as a reliable method for constraining some parameters of a given model [Phys. Rev. D \textbf{92} (2015) 126005, Eur. Phys. J. C \textbf{76} (2016) 100]. In this letter we calculate the…
In this letter, we fill a hole in the existing literature about disordered quantum spin systems generated by a random local interaction $\{\mathfrak{h}(Z)\}_{Z\Subset \mathbb{Z}^\nu}$ satisfying a statistical version of translation…
We study a configuration model on bipartite planar maps in which, given $n$ even integers, one samples a planar map with $n$ faces uniformly at random with these face degrees. We prove that when suitably rescaled, such maps always admit…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process.…
It has been proposed that the states of fully many-body localized systems can be described in terms of conserved local pseudospins. Due to the multitude of ways to define these, the explicit identification of the optimally local pseudospins…
Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in…
We investigate the conditional distributions of two Banach space valued, jointly Gaussian random variables. In particular, we show that these conditional distributions are again Gaussian and that their means and covariances can be…
The fate of spin-charge separation beyond the low energy remains elusive up to now. Here we develop a microscopic theory of the correlation functions using the strong coupling expansion of the Hubbard model and demonstrate its validity down…
We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model…