The Laplacian Growth (LG) model is known as a universality class of scale-free aggregation models in two dimensions, characterized by classical integrability and featuring finite-time boundary singularity formation. A discrete counterpart, Diffusion-Limited Aggregation (or DLA), has a similar local growth law, but significantly different global behavior. For both LG and DLA, a proper description for the scaling properties of long-time solutions is not available yet. In this note, we outline a possible approach towards finding the correct theory yielding a regularized LG and its relation to DLA.

翻译：拉普拉斯生长（LG）模型被视为二维无标度聚集模型的普适类，其特点是具有经典可积性并伴随有限时间边界奇点形成。其离散对应物——扩散受限聚集（DLA）模型具有相似的局部生长规律，但全局行为显著不同。对于LG和DLA，目前尚无对长时间解标度性质的恰当描述。本文概述了一种可能的研究路径，旨在建立正则化LG的正确理论及其与DLA的关系。