Related papers: Deciphering Non-Gaussianity of Diffusion Based on …
Diffusion Models (DMs) are powerful generative models that add Gaussian noise to the data and learn to remove it. We wanted to determine which noise distribution (Gaussian or non-Gaussian) led to better generated data in DMs. Since DMs do…
Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is…
Understanding the non-local pressure contributions and viscous effects on the small-scale statistics remains one of the central challenges in the study of homogeneous isotropic turbulence. Here we address this issue by studying the impact…
In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…
We derive a Thermodynamic Uncertainty Relation bounding the mean squared displacement of a Gaussian process with memory, driven out of equilibrium by unbalanced thermal baths and/or by external forces. Our bound is tighter with respect to…
Caustics in the dynamics of heavy particles in turbulence accelerate particle collisions. The rate $\mathscr{J}$ at which these singularities form depends sensitively on the Stokes number St, the non-dimensional inertia parameter. Exact…
Following the discovery of the CMB, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today.…
Performance guarantees for compression in nonlinear models under non-Gaussian observations can be achieved through the use of distributional characteristics that are sensitive to the distance to normality, and which in particular return the…
We consider the problem of probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities.…
The dynamics of dense stabilized emulsions presents a rich phenomenology including chaotic emulsification, non-Newtonian rheology and ageing dynamics at rest. Macroscopic rheology results from the complex droplet microdynamics and, in turn,…
Measures of the non-Gaussianity of a random field depend on how accurately one is able to measure the field. If a signal measured at a certain point is to be averaged with its surroundings, or coarse-grained, the magnitude of its…
Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point…
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that…
We numerically investigate non-Gaussianities in the late-time cosmological density field in Fourier space. We explore various statistics, including the two-point and three-point probability distribution function (PDF) of phase and modulus,…
This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions,…
We examine the multi--point velocity field for non--Gaussian models as a probe of non--Gaussian behavior. The two--point velocity correlation is not a useful indicator of a non--Gaussian density field, since it depends only on the power…
Living cells are known to generate non-Gaussian active fluctuations significantly larger than thermal fluctuations owing to various active processes. Understanding the effect of these active fluctuations on various physicochemical…
Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of significant non-Gaussianity would thus have profound implications for…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
Recent studies unveiled the Fickian yet non-Gaussian (FNG) dynamics of many soft matter systems and suggested this phenomenon as a general characteristic of the diffusion in complex fluids. In particular, it was shown that the distribution…