• Corpus ID: 221516155

The critical one-dimensional multi-particle DLA

  title={The critical one-dimensional multi-particle DLA},
  author={Dor Elboim and Danny Nam and Allan Sly},
  journal={arXiv: Probability},
We study one-dimensional multi-particle Diffusion Limited Aggregation (MDLA) at its critical density $\lambda=1$. Previous works have verified that the size of the aggregate $X_t$ at time $t$ is $t^{1/2}$ in the subcritical regime and linear in the supercritical regime. This paper establishes the conjecture that the growth rate at criticiality is $t^{2/3}$. Moreover, we derive the scaling limit proving that $$\big\{ t^{-2/3}X_{st} \big\}_{s\geq 0} \overset{d}{\rightarrow} \Big\{ \int_0^s Z_u… 

Figures and Tables from this paper

Spread of infections in a heterogeneous moving population

We consider a model where an infection moves through a collection of particles performing independent random walks. In this model, Kesten and Sidoravicius established linear growth of the infected

Scaling limits of external multi-particle DLA on the plane and the supercooled Stefan problem

. We consider (a variant of) the external multi-particle diffusion-limited aggregation (MDLA) process of Rosenstock and Marquardt on the plane. Based on the findings of [8], [12], [11] in one space



Minimal Conditions for Weak Convergence to a Diffusion Process on the Line

Criticality of a Randomly-Driven Front

AbstractConsider an advancing ‘front’ $${R(t) \in \mathbb{Z}_{\geqq 0}}$$R(t)∈Z≧0 and particles performing independent continuous time random walks on $${ (R(t), \infty) \cap \mathbb{Z}}$$(R(t),∞)∩Z.

One-dimensional Multi-particle DLA -- a PDE approach

In the present note we analyze the one-dimensional multi-particle diffusion limited aggregation (MDLA) model: the initial number of particles at each positive integer site has Poisson distribution

On One-Dimensional Multi-Particle Diffusion Limited Aggregation

  • A. Sly
  • Physics
    Progress in Probability
  • 2020
We prove that the one dimensional Multi-Particle Diffusion Limited Aggregation model has linear growth whenever the particle density exceeds 1 answering a question of Kesten and Sidoravicius. As a

Large Deviations of the Front in a one dimensional model of X + Y ! 2X

We investigate the probabilities of large deviations for the position of the front in a stochastic model of the reaction X + Y → 2X on the integer lattice in which Y particles do not move while X

Random growth in a tessellation

  • D. Richardson
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1973
Let S be n dimensional Euclidean space and let T be a division of S into cells. Assume that each cell must be either white or black at any time t. At time 0 the cell at the origin, α0, is black and

On Tail Probabilities for Martingales

Hitting probabilities of random walks on Zd

Multiparticle diffusive fractal aggregation

Formation of fractal clusters and networks by irreversible diffusion-limited aggregation

A model for diffusion-controlled aggregation in which growing clusters as well as individual particles are mobile has been investigated. Two versions of the model in which the cluster diffusion