Related papers: Fluctuation universality for a class of directed s…
Probabilistic diffusion models enjoy increasing popularity in the deep learning community. They generate convincing samples from a learned distribution of input images with a wide field of practical applications. Originally, these…
A lattice-based model for continuum percolation is applied to the case of randomly located, partially aligned sticks with unequal lengths in 2D which are allowed to cross each other. Results are obtained for the critical number of sticks…
We consider a stochastic Laplacian growth problem in the framework of normal random matrices. In the large $N$ limit the support of eigenvalues of random matrices is a planar domain with a sharp boundary which evolves under a change in the…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
In sufficiently high spatial dimensions, the formation of the amorphous (i.e. random) solid state of matter, e.g., upon sufficent crosslinking of a macromolecular fluid, involves particle localization and, concommitantly, the spontaneous…
We consider systems of diffusion processes ("particles") interacting through their ranks (also referred to as "rank-based models" in the mathematical finance literature). We show that, as the number of particles becomes large, the process…
We report sets of precise and reproducible measurements on the static pressure at the bottom of a granular column. We make a quantitative analysis of the pressure saturation when the column height is increased. We evidence a great…
In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…
Atmospheric flows exhibit self-similar fractal space-time fluctuations on all space-time scales in association with inverse power law distribution for power spectra of meteorological parameters such as wind, temperature, etc., and thus…
We investigate velocity probability distribution functions (PDF) of sheared hard-sphere suspensions. As observed in our Stokes flow simulations and explained by our single-particle theory, these PDFs can show pronounced deviations from a…
We consider a fiber bundle model with a equal load sharing and uniformly distributed breakdown thresholds. A unified probability-theoretic approach was used to describe bundle under continuous and discrete load increase. It was shown that…
Experimental and theoretical studies are made of Brownian particles trapped in a periodic potential, which is very slightly tilted due to gravity. In the presence of fluctuations, these will trigger a measurable average drift along the…
We investigate the total asymmetric exclusion process by analyzing the dynamics of the shock. Within this approach we are able to calculate the fluctuations of the number of particles and density profiles not only in the stationary state…
We report the structure of transient fluctuations in the liquid phase of a two-dimensional system that exhibits several ordered phases with different symmetries. The density-temperature phase diagram of the system studied, composed of…
Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…
A driven granular material, e.g. a vibrated box full of sand, is a stationary system which may be very far from equilibrium. The standard equilibrium statistical mechanics is therefore inadequate to describe fluctuations in such a system.…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
We study the average shape of fluctuations for subdiffusive processes, i.e., processes with uncorrelated increments but where the waiting time distribution has a broad power-law tail. This shape is obtained analytically by means of a…
We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations…
This paper deals with a new class of random flights $\underline{\bf X}_d(t),t>0,$ defined in the real space $\mathbb{R}^d, d\geq 2,$ characterized by non-uniform probability distributions on the multidimensional sphere. These random motions…