Artem Borisov

Local convergence in the t-deformed polynuclear growth model (t-PNG)

Polynuclear growth, or PNG, is a well-studied random model. It represents a growing surface, which starts from a horizontal line. Height increments randomly appear as points on this surface; these events are called “nucleations”. Increments propagate with unit velocity, forming “growth islands”. Whenever 2 islands meet, they merge. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class; in particular, the height exhibits cube root fluctuations. It is also strongly related to longest increasing subsequences of random permutations and the patience sorting algorithm.

t-deformed PNG (or just t-PNG) is a modification of this model, in which island merging events produce new nucleations with probability t. It is also proven to lie in the KPZ class and can be interpreted as patience sorting “with errors”. In our work with Márton Balázs, Ruby Bestwick, Elnur Emrah, and Jessica Jay, we discuss this model and prove its stabilisation. The preprint can be found at https://arxiv.org/abs/2512.10550.