Related papers: Tight space-noise tradeoffs in computing the ergod…
This paper establishes the ergodicity in $H^\nn,\nn=\lfloor\frac{d}{2}+1\rfloor$ of the viscous scalar conservation laws on torus $\mT^d$ with general polynomial flux and a degenerate noise. The noise could appear in as few as several…
We establish the existence, uniqueness and attraction properties of an ergodic invariant measure for the Boussinesq Equations in the presence of a degenerate stochastic forcing acting only in the temperature equation and only at the largest…
Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In…
We study invariant boundary conditions for one dimensional discrete Gaussian Markov processes, basic toy models of spatial Markov processes in statistical mechanics. More precisely, we give a decomposition of boundary objects in a non…
This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in…
We establish general quantitative conditions for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise in variational formulation resulting in the existence of a unique invariant probability measure…
The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M…
In the present paper we give proof that the information-transmission capacity of the approximate position measurement with the oscillator energy constraint, which underlies noisy Gaussian homodyning in quantum optics, is attained on…
The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered.…
Intrinsic noise in objective function and derivatives evaluations may cause premature termination of optimization algorithms. Evaluation complexity bounds taking this situation into account are presented in the framework of a deterministic…
We introduce an additive Gaussian process framework accounting for monotonicity constraints and scalable to high dimensions. Our contributions are threefold. First, we show that our framework enables to satisfy the constraints everywhere in…
For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structrue of the space of invariant measures: The ergodic measures of intermediate entropies and…
We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…
A measured solenoid is a laminated space endowed with a tranversal measure invariant by holonomy, as defined in arXiv:0910.2836. A measured solenoid immersed in a smooth manifold produces a closed current (known as generalized…
We establish the unique ergodicity of a fully discrete scheme for monotone SPDEs with polynomial growth drift and bounded diffusion coefficients driven by multiplicative white noise. The main ingredient of our method depends on the…
We study ergodic-theoretic properties of coded shift spaces. A coded shift space is defined as a closure of all bi-infinite concatenations of words from a fixed countable generating set. We derive sufficient conditions for the uniqueness of…
We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to…
Questions of noise stability play an important role in hardness of approximation in computer science as well as in the theory of voting. In many applications, the goal is to find an optimizer of noise stability among all possible partitions…
We consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary probabilistic distribution. We prove the maximal and…
This paper investigates the stochastic Cahn-Hilliard equation (SCHE) driven by additive space-time white noise. We first refine the analytical ergodic theory by proving that the continuum equation admits a unique invariant measure in the…