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In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…

Probability · Mathematics 2007-05-23 L. V. Bogachev , Z. G. Su

We show that Internal Diffusion Limited Aggregation (IDLA) on $\mathbb{Z}^d$ has near optimal Cheeger constant when the growing cluster is large enough. This implies, through a heat kernel lower bound derived previously in [H], that simple…

Probability · Mathematics 2019-04-18 Ruojun Huang

We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible…

Statistical Mechanics · Physics 2009-10-31 Raissa M. D'Souza , Norman H. Margolus

We consider a random growth model based on the IDLA protocol with sources in a hyperplane of $Z^d$ . We provide a stabilization result and a shape theorem generalizing [7] in any dimension by introducing new techniques leading to a rough…

Probability · Mathematics 2025-12-11 Nicolas Chenavier , David Coupier , Keenan Penner , Arnaud Rousselle

We consider a system of $N$ disordered mean-field interacting diffusions within spatial constraints: each particle $\theta_i$ is attached to one site $x_i$ of a periodic lattice and the interaction between particles $\theta_i$ and…

Probability · Mathematics 2020-01-16 Eric Luçon , Wilhelm Stannat

We propose a simple model of columnar growth through {\it diffusion limited aggregation} (DLA). Consider a graph $G_N\times\N$, where the basis has $N$ vertices $G_N:=\{1,\dots,N\}$, and two vertices $(x,h)$ and $(x',h')$ are adjacent if…

Probability · Mathematics 2015-11-24 A. Asselah , E. Cirillo , E. Scoppola , B. Scoppola

In the classical model of Diffusion Limited Aggregation (DLA), introduced by Witten and Sander, the process begins with a single particle cluster placed at the origin of a space, and then, one at a time, particles make a random walk from…

Probability · Mathematics 2026-04-29 Colin Cooper , Alan Frieze

We study the droplet that results from conditioning the subcritical Fortuin-Kasteleyn planar random cluster model on the presence of an open circuit Gamma_0 encircling the origin and enclosing an area of at least (or exactly) n^2. We…

Probability · Mathematics 2011-06-14 Alan Hammond

The Internal Diffusion Limited Aggregation has been introduced by Diaconis and Fulton in 1991. It is a growth model defined on an infinite set and associated to a Markov chain on this set. We focus here on sets which are finitely generated…

Probability · Mathematics 2007-05-23 Sebastien Blachere , Sara Brofferio

We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process…

chao-dyn · Physics 2009-10-31 Benny Davidovich , Itamar Procaccia

We establish quantitative spherical shape theorems for rotor-router aggregation and abelian sandpile growth on the graphical Sierpinski gasket ($SG$) when particles are launched from the corner vertex. In particular, the abelian sandpile…

Mathematical Physics · Physics 2020-12-02 Joe P. Chen , Jonah Kudler-Flam

In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation…

Statistical Mechanics · Physics 2007-05-23 S. G. Alves , S. C. Ferreira

We discuss the scaling of characteristic lengths in diffusion limited aggregation (DLA) clusters in light of recent developments using conformal maps. We are led to the conjecture that the apparently anomalous scaling of lengths is due to…

Statistical Mechanics · Physics 2009-10-31 E. Somfai , L. M. Sander , R. C. Ball

We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the…

Mathematical Physics · Physics 2014-08-26 Jeffrey Kuan

Diffusion Limited Aggregation (DLA) has served for forty years as a paradigmatic example for the creation of fractal growth patterns. In spite of thousands of references no exact result for the fractal dimension $D$ of DLA is known. In this…

Statistical Mechanics · Physics 2021-02-17 Eviatar B. Procaccia , Itamar Procaccia

It was recently suggested by Boldyrev & Gwinn that the characteristics of radio scintillations from distant pulsars are best understood if the interstellar electron-density fluctuations that cause the time broadening of the radio pulses…

Astrophysics · Physics 2010-11-11 Stanislav Boldyrev , Arieh Konigl

In analogy to recent results on non-universal roughening in surface growth [Lam and Sander, Phys. Rev. Lett. {\bf 69}, 3338 (1992)], we propose a variant of diffusion-limited aggregation ($DLA$) in which the radii of the particles are…

Condensed Matter · Physics 2007-05-23 P. Ossadnik , C. -H. Lam , L. M. Sander

We study the fluctuations of smooth linear statistics of Laplace eigenvalues of compact hyperbolic surfaces lying in short energy windows, when averaged over the moduli space of surfaces of a given genus. The average is taken with respect…

Spectral Theory · Mathematics 2023-01-03 Zeév Rudnick , Igor Wigman

An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the flow field (vortices) and in the density field (clusters), driven by unstable fluctuations. Their spatial correlations, as measured in…

Statistical Mechanics · Physics 2009-10-30 J. A. G. Orza , R. Brito , T. P. C. Van Noije , M. H. Ernst

In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the…

Statistical Mechanics · Physics 2010-09-09 S. G. Alves , S. C. Ferreira