Related papers: Containing Internal Diffusion Limited Aggregation
We investigate the maximal non-critical cluster in a big box in various percolation-type models. We investigate its typical size, and the fluctuations around this typical size. The limit law of these fluctuations are related to maxima of…
We extend the conformal mapping approach elaborated for the radial Diffusion Limited Aggregation model (DLA) to the cylindrical geometry. We introduce in particular a complex function which allows to grow a cylindrical cluster using as…
We expand upon a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these…
In-context Learning (ICL) is an emerging few-shot learning paradigm on Language Models (LMs) with inner mechanisms un-explored. There are already existing works describing the inner processing of ICL, while they struggle to capture all the…
We analyse the density of states of the random graph Laplacian in the percolating regime. A symmetry argument and knowledge of the density of states in the nonpercolating regime allows us to isolate the density of states of the percolating…
For a general class of percolation models with long-range correlations on $\mathbb Z^d$, $d\geq 2$, introduced in arXiv:1212.2885, we establish regularity conditions of Barlow arXiv:math/0302004 that mesoscopic subballs of all large enough…
Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…
In soft matter system controlling the structure of the amorphous materials have been a key challenge. In this work we have modeled irreversible diffusion limited cluster aggregation of binary colloids, which serves as a model for chemical…
The diffuse intracluster light (ICL) contains a significant fraction of the total stellar mass in clusters of galaxies, and contributes in roughly equal proportion as the hot intra-cluster medium (ICM) to the total baryon content of…
We develop the skeleton algorithm to define the number of main branches $N_b$ of diffusion-limited aggregation (DLA) clusters. The skeleton algorithm provides a systematic way to remove dangling side branches of the DLA cluster and has…
We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find…
Context. The intracluster light (ICL) comprises stars that are not bound to individual galaxies within a galaxy cluster, and it provides insights into the cluster mass distribution, evolutionary history, and dynamical state. Aims. We study…
The method of iterated conformal maps for the study of Diffusion Limited Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and related processes. We emphasize the fundamental difference between these processes: DLA…
The main focus of this article concerns the strongly percolative regime of the vacant set of random interlacements on $ \mathbb{Z}^d$, with $d \ge 3$. We investigate the occurrence in a large box of an excessive fraction of sites that get…
We consider long-range percolation on $\mathbb{Z}^d$, where the probability that two vertices at distance $r$ are connected by an edge is given by $p(r)=1-\exp[-\lambda(r)]\in(0,1)$ and the presence or absence of different edges are…
Intracluster light (ICL) is a key component of galaxy clusters, with the potential to trace their dynamical assembly histories and the underlying dark matter distribution. Despite these prospects, its faint nature makes a consensus on its…
This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for…
The diffuse intragroup light (IGL) is a pervasive feature of galaxy groups consisting of an extended low-surface-brightness component that permeates the intergalactic medium of these galaxy associations. It is primarily formed by stars…
We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to p_c with an inverse power, \lambda, of the distance to the origin. Assuming the existence of…
Large-scale 3D generative models require substantial computational resources yet often fall short in capturing fine details and complex geometries at high resolutions. We attribute this limitation to the inefficiency of current…