Related papers: Containing Internal Diffusion Limited Aggregation
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…
In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…
The controllable generation of diffusion models aims to steer the model to generate samples that optimize some given objective functions. It is desirable for a variety of applications including image generation, molecule generation, and…
In this paper, we consider a non-homogeneous discrete-time Markov chain which can be seen as a toy model for the growth of the arms of the DLA (Diffusion limited aggregation) process in a sub-linear wedge. It is conjectured that in a thin…
Discrete diffusion models have emerged as a powerful class of models and a promising route to fast language generation, but practical implementations typically rely on factored reverse transitions ignoring cross-token dependencies and…
Diffusion-limited aggregation is consistent with simple scaling. However, strong subdominant terms are present, and these can account for various earlier claims of anomalous scaling. We show this in detail for the case of multiscaling.
A large fraction of the stellar mass in galaxy clusters is thought to be contained in the diffuse low surface brightness intracluster light (ICL). Being bound to the gravitational potential of the cluster rather than any individual galaxy,…
We consider the problem of sampling distributions stemming from non-convex potentials with Unadjusted Langevin Algorithm (ULA). We prove the stability of the discrete-time ULA to drift approximations under the assumption that the potential…
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution…
We study long-range Bernoulli percolation on $\mathbb{Z}^d$ in which each two vertices $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta \|x-y\|^{-d-\alpha})$. It is a theorem of Noam Berger (CMP, 2002) that if…
We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers…
The statistical behavior of the size (or mass) of the largest cluster in subcritical percolation on a finite lattice of size $N$ is investigated (below the upper critical dimension, presumably $d_c=6$). It is argued that as $N \to \infty$…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
Independent sets in graphs are sets of vertices containing no neighbors, and they represent a canonical spin system with hardcore constraints. Of particular interest is the setting of the boolean hypercube, where counting independent sets…
We study independent long-range percolation on $\mathbb{Z}^d$ where the vertices $x$ and $y$ are connected with probability $1-e^{-\beta\|x-y\|^{-d-\alpha}}$ for $\alpha > 0$. Provided the critical exponents $\delta$ and $2-\eta$ defined by…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
In the digital age, advanced image editing tools pose a serious threat to the integrity of visual content, making image forgery detection and localization a key research focus. Most existing Image Manipulation Localization (IML) methods…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
Diffuse intracluster light (ICL) has now been observed in nearby and in intermediate redshift clusters. Individual intracluster stars have been detected in the Virgo and Coma clusters and the first color-magnitude diagram and velocity…