Related papers: Dimension-decaying diffusion processes as the scal…

We investigate the process of dimensional reduction of one spatial dimension in a thermal scalar field model defined in $D$ dimensions (inverse temperature and $D-1$ spatial dimensions). We obtain that a thermal model in $D$ dimensions with…

We extend one dimensional asymmetric simple exclusion process (ASEP) to a surface and show that the effect of transverse diffusion is to induce a continuous phase transition from a constant density phase to a maximal current phase as the…

Epitaxial growth methods are a key technology used in producing large-area thin films on substrates but as a result of various factors controlling growth processes the rational optimization of growth conditions is rather difficult.…

We study diffusion processes that are stopped or reflected on the boundary of a domain. The generator of the process is assumed to contain two parts: the main part that degenerates on the boundary in a direction orthogonal to the boundary…

We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…

Starting from a sequence of independent Wright-Fisher diffusion processes on $[0,1]$, we construct a class of reversible infinite dimensional diffusion processes on $\DD_\infty:= \{{\bf x}\in [0,1]^\N: \sum_{i\ge 1} x_i=1\}$ with GEM…

We study diffusion-controlled single-species annihilation with sparse initial conditions. In this random process, particles undergo Brownian motion, and when two particles meet, both disappear. We focus on sparse initial conditions where…

We investigate the saturation regime of the condensing symmetric inclusion process on the discrete one-dimensional torus in the thermodynamical limit. In this regime, the total mass concentrates on a finite number of sites, forming…

We investigate the late coarsening stages of one dimensional adsorption processes with diffusional relaxation. The nonequilibrium domain size distribution is studied by means of the field theory associated to the stochastic evolution. An…

The divergence of perturbative expansions for the vast majority of macroscopic systems, which follows from Dyson's collapse argument, prevents Feynman's diagrammatic technique from being directly used for controllable studies of strongly…

Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…

The Sierpinski gasket is known to support an exotic stochastic process called the asymptotically one-dimensional diffusion. This process displays local anisotropy, as there is a preferred direction of motion which dominates at the…

The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…

We introduce a continuum percolation model defined on the points of a d-dimensional homogeneous Poisson process. Each Poisson point is connected to all points within its connection range, which depends on the distances to the other Poisson…

This study is concerned with the decay behaviour of a passive scalar $\theta$ in three-dimensional flows having bounded velocity gradients. Given an initially smooth scalar distribution, the decay rate $d<\theta^2>/dt$ of the scalar…

We establish a general analytic framework for determining the AF-martingale dimension of diffusion processes associated with strongly local regular Dirichlet forms on metric measure spaces. While previous approaches typically relied on…

We derive an anomalous, sub-diffusive scaling limit for a one-dimensional version of the Mott random walk. The limiting process can be viewed heuristically as a one-dimensional diffusion with an absolutely continuous speed measure and a…

We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…

Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifold learning, denoising, clustering, and visualization of…

We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s)…