• Corpus ID: 221516155

# The critical one-dimensional multi-particle DLA

@article{Elboim2020TheCO,
title={The critical one-dimensional multi-particle DLA},
author={Dor Elboim and Danny Nam and Allan Sly},
journal={arXiv: Probability},
year={2020}
}
• Published 6 September 2020
• Mathematics
• 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 $$\big\{ t^{-2/3}X_{st} \big\}_{s\geq 0} \overset{d}{\rightarrow} \Big\{ \int_0^s Z_u… 2 Citations ## Figures and Tables from this paper • Mathematics • 2021 We consider a model where an infection moves through a collection of particles performing independent random walks. In this model, Kesten and Sidoravicius established linear growth of the infected • Mathematics • 2021 . We consider (a variant of) the external multi-particle diﬀusion-limited aggregation (MDLA) process of Rosenstock and Marquardt on the plane. Based on the ﬁndings of [8], [12], [11] in one space ## References SHOWING 1-10 OF 27 REFERENCES • Mathematics Archive for Rational Mechanics and Analysis • 2019 AbstractConsider an advancing ‘front’$${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.
• Mathematics
• 2017
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
• 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
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
• 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
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