Related papers: Directed Diffusion-Limited Aggregation
In this article, we consider two models of directed polymers in random environment: a discrete model and a continuous model. We consider these models in dimension greater or equal to 3 and we suppose that the normalized partition function…
The continuum random cluster model is defined as a Gibbs modification of the stationary Boolean model in $\mathbb{R}^d$ with intensity $z>0$ and the law of radii $Q$. The formal unormalized density is given by $q^{N_{cc}}$ where $q>0$ is a…
Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…
Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward…
In this paper we consider a model for the diffusion of a population in a strip-shaped field, where the growth of the species is governed by a Fisher-KPP equation and which is bounded on one side by a road where the species can have a…
In this work I show how a diffusion-advection equation in three space-dimensions may have its advection term weakly limited to a velocity field localized to a moving curve. This is rigorously accomplished through the technique of…
Diffusion models exhibit excellent sample quality, but existing guidance methods often require additional model training or are limited to specific tasks. We revisit guidance in diffusion models from the perspective of variational inference…
Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…
We investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on $\mathbf{Z}^2$ with infinitely many sources that are the points of the vertical axis…
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…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
Discrete diffusion models are a new class of text generators that offer advantages such as bidirectional context use, parallelizable generation, and flexible prompting compared to autoregressive models. However, a critical limitation of…
We derive analytic expressions for the possibility, probability, and expected size of global spreading events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed…
In this paper, we present results of extensive Monte Carlo simulations of diffusion-limited aggregation (DLA) with a seed placed on an attractive plane as a simple model in connection with the electrical double layers. We compute the…
We propose a revision of the classic mean-field approach of diffusion-limited aggregation (DLA) model originally introduced by Witten and Sander [Phys. Rev. Lett. 47, 1400 (1981)]. The derived nonlinear mean-field equations providing…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…
Crowd counting is an important problem in computer vision due to its wide range of applications in image understanding. Currently, this problem is typically addressed using deep learning approaches, such as Convolutional Neural Networks…
We consider a model of aggregation, both diffusion-limited and ballistic, based on the Cayley tree. Growth is from the leaves of the tree towards the root, leading to non-trivial screening and branch competition effects. The model exhibits…
In this paper, we propose a finite-volume scheme for aggregation-diffusion equations based on a Scharfetter--Gummel approximation of the quadratic, nonlocal flux term. This scheme is analyzed concerning well-posedness and convergence…