Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of and stick to the interface at the first point of contact, causing it to grow. We consider an alternative version of this model in which the blocks have random heights which are i.i.d. and heavy tailed, and where each block sticks to the interface at the first point of contact with probability p (otherwise, it falls straight down until it lands on a block belonging to the interface). We study scaling limits of the resulting interface for the different values of p and show that there is a phase transition as p goes from 1 to 0.
The work of S.S. was supported in part at the Technion by a fellowship from the Lady Davis Foundation, the Israeli Science Foundation grants no. 1723/14 and 765/18, Fondecyt Grant no. 11200690, Iniciativa Científica Milenio “Modelos Estocásticos de Sistemas Complejos y Desordenados” and by the United States-Israel Binational Science Foundation (BSF) Grant no. 2018330.
This paper is dedicated to the memory of author Francis Comets, who passed away in June 2022
The authors are immensely grateful to Vladas Sidoravicius for encouraging us to take on this problem and for the numerous enlightening discussions we had together during our joint time at NYU Shanghai.
"Scaling limit of the heavy tailed ballistic deposition model with p-sticking." Ann. Probab. 51 (5) 1870 - 1931, September 2023. https://doi.org/10.1214/23-AOP1635