Related papers: Containing Internal Diffusion Limited Aggregation
We introduce Gradient Flow Aggregation (GFA), a random growth model. Given a set of existing particles $\left\{x_1, \dots, x_n\right\} \subset \mathbb{R}^2$, a new particle arrives from a random direction at $\infty$ and flows in direction…
We consider the constrained-degree percolation (CDP) model on the hypercubic lattice. This is a continuous-time percolation model defined by a sequence $(U_e)_{e\in\mathcal{E}^d}$ of i.i.d. uniform random variables and a positive integer…
We present a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions. Key steps are understanding how these models interrelate when the ultra-violet cut-off strategy is…
A parallel algorithm for ``diffusion-limited aggregation'' (DLA) is described and analyzed from the perspective of computational complexity. The dynamic exponent z of the algorithm is defined with respect to the probabilistic parallel…
An early (and influential) scaling relation in the multifractal theory of Diffusion Limited Aggregation(DLA) is the Turkevich-Scher conjecture that relates the exponent \alpha_{min} that characterizes the ``hottest'' region of the harmonic…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
We consider the following problem in one-dimensional diffusion-limited aggregation (DLA). At time $t$, we have an "aggregate" consisting of $\Bbb{Z}\cap[0,R(t)]$ [with $R(t)$ a positive integer]. We also have $N(i,t)$ particles at $i$,…
Generative recommendation represents each item as a semantic ID, i.e., a sequence of discrete tokens, and generates the next item through autoregressive decoding. While effective, existing autoregressive models face two intrinsic…
Controllable layout generation aims at synthesizing plausible arrangement of element bounding boxes with optional constraints, such as type or position of a specific element. In this work, we try to solve a broad range of layout generation…
The random Lorentz gas (RLG) is a minimal model for transport in disordered media. Despite the broad relevance of the model, theoretical grasp over its properties remains weak. For instance, the scaling with dimension d of its localization…
In an attempt to find generic features on the fractal growth of Au films deposited on Ru(001), a simple simulation model based on irreversible diffusion-limited aggregation (DLA) is discussed. Highly irregular two-dimensional dentritic…
Fine-grained clustering is a practical yet challenging task, whose essence lies in capturing the subtle differences between instances of different classes. Such subtle differences can be easily disrupted by data augmentation or be…
We propose Inner Loop Feedback (ILF), a novel approach to accelerate diffusion models' inference. ILF trains a lightweight module to predict future features in the denoising process by leveraging the outputs from a chosen diffusion backbone…
In the Constrained-degree percolation model on a graph $(\mathbb{V},\mathbb{E})$ there are a sequence, $(U_e)_{e\in\mathbb{E}}$, of i.i.d. random variables with distribution $U[0,1]$ and a positive integer $k$. Each bond $e$ tries to open…
Percolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density $\lambda_c^{(d)}$ for $d$-dimensional Poisson random geometric…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
We introduce Interleaved Gibbs Diffusion (IGD), a novel generative modeling framework for discrete-continuous data, focusing on problems with important, implicit and unspecified constraints in the data. Most prior works on discrete and…
In this paper, we introduce the stationary harmonic measure in the upper half plane. By bounding this measure, we are able to define both the discrete and continuous time diffusion limit aggregation (DLA) in the upper half plane with…
We derive lower bounds on the maximal rates for multiple packings in high-dimensional Euclidean spaces. Multiple packing is a natural generalization of the sphere packing problem. For any $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $, a multiple…