# 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} }

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…

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