Related papers: Bargmann-Fock percolation is noise sensitive
This paper describes an extension of the BFGS and L-BFGS methods for the minimization of a nonlinear function subject to errors. This work is motivated by applications that contain computational noise, employ low-precision arithmetic, or…
We study a noise-induced bifurcation in the vicinity of the threshold by using a perturbative expansion of the order parameter, called the Poincar\'e-Lindstedt expansion. Each term of this series becomes divergent in the long time limit if…
Arguments based on general principles of quantum mechanics suggest that a minimum length or time associated with Planck-scale unification may entail a new kind of observable uncertainty in the transverse position of macroscopically…
Let $\eta$ be a Poisson random measure (defined on some Polish space), and let $F(\eta)$ be a square-integrable functional of $\eta$. In this paper we define and study a new notion of {\it spectral point process} associated with $F(\eta)$,…
Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete…
Waves and oscillations are commonly observed in the dynamics of self-driven agents such as pedestrians or vehicles. Interestingly, many factors may perturb the stability of space homogeneous streaming, leading to the spontaneous formation…
We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavy-tailed increments, and the transition probability density of the…
Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…
Statistical early warning signs can be used to identify an approaching bifurcation in stochastic dynamical systems and are now regularly employed in applications concerned with the identification of potential rapid, non-linear change or…
We prove the hardness of weakly learning halfspaces in the presence of adversarial noise using polynomial threshold functions (PTFs). In particular, we prove that for any constants $d \in \mathbb{Z}^+$ and $\varepsilon > 0$, it is NP-hard…
Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as…
The Planck Low Frequency Instrument will recover polarization by differencing the outputs from radiometers sensitive to orthogonal polarizations. We contrast the systematic errors that afflict such a system with those that affect…
In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
This article establishes the cutoff phenomenon in the Wasserstein distance for systems of nonlinear ordinary differential equations with a unique coercive stable fixed point subject to general additive Markovian noise in the limit of small…
We study oriented percolation on random causal triangulations, those are random planar graphs obtained roughly speaking by adding horizontal connections between vertices of an infinite tree. When the underlying tree is a geometric…
We consider the Busemann process in planar directed first passage percolation. We extend existing techniques to establish the existence of the process in our setting and determine its distribution in a number of integrable models. As…
Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these…
This paper derives non-asymptotic error bounds for nonlinear stochastic approximation algorithms in the Wasserstein-$p$ distance. To obtain explicit finite-sample guarantees for the last iterate, we develop a coupling argument that compares…
We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds…