Related papers: Shot noise distributions and selfdecomposability
Given a factorization of an image into a sum of linear components, we present a zero-shot method to control each individual component through diffusion model sampling. For example, we can decompose an image into low and high spatial…
Many classical variables (statistics) are selfdecomposable. They admit the random integral representations via L\'evy processes. In this note are given formulas for their background driving distribution functions (BDDF). This may be used…
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
We argue, physically and formally, that existing diffusive models of noise yield inaccurate microscopic descriptions of nonequilibrium current fluctuations. The theoretical shortfall becomes pronounced in quantum-confined metallic systems,…
A recent theory is reviewed for the shot noise of coherent radiation propagating through a random medium. The Fano factor P/I (the ratio of the noise power and the mean transmitted current) is related to the scattering matrix of the medium.…
We prove an exact relationship between the optimal denoising function and the data distribution in the case of additive Gaussian noise, showing that denoising implicitly models the structure of data allowing it to be exploited in the…
A notion of disturbance propagation stability is defined for dynamical network processes, in terms of decrescence of an input-output energy metric along cutsets away from the disturbance source. A characterization of the disturbance…
We show that the `shot noise' bias in angular clustering power spectra observed from discrete samples of points is not noise, but rather a known additive contribution that naturally arises due to degenerate pairs of points. In particular,…
Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric…
Fluctuations pose fundamental limitations in making sensitive measurements, yet at the same time, noise unravels properties that are inaccessible at the level of the averaged signal. In electronic devices, shot noise arises from the…
Prediction models can perform poorly when deployed to target distributions different from the training distribution. To understand these operational failure modes, we develop a method, called DIstribution Shift DEcomposition (DISDE), to…
Dilative semistability extends the notion of semi-selfsimilarity for infinitely divisible stochastic processes by introducing an additional scaling in the convolution exponent. It is shown that this scaling relation is a natural extension…
We characterize all possible independent symmetric alpha-stable (SaS) components of an SaS process, 0<alpha<2. In particular, we focus on stationary SaS processes and their independent stationary SaS components. We also develop a parallel…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Flow and Diffusion Distributed Structures (FDS) are stationary spatially periodic patterns that can be observed in reaction-diffusion-advection systems. These structures arise when the flow rate exceeds a certain bifurcation point provided…
In this paper, we investigate in a unified way the structural properties of solutions to inverse problems. These solutions are regularized by the generic class of semi-norms defined as a decomposable norm composed with a linear operator,…
We study synchronization processes in networks of slightly non identical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in…
Under natural assumptions, an unstable equilibrium of a difference equation can be stabilized by a bounded multiplicative noise, identically distributed at each step. This includes stabilization of an otherwise unstable positive equilibrium…
In this paper we find and develop a stochastic integral representation for the class of strictly stable distributions. We establish an explicit relationship between stochastic integral and shot-noise series representations of strictly…
We provide an example for stabilization by noise. Our approach does not rely on monotonicity arguments due to the presence of higher order differential operators or mixing properties of the system as the noise might be highly degenerate. In…