Exponential Clogging Time for a One Dimensional DLA

Abstract

In this paper a simple DLA type model is analyzed. In (Benjamini and Yadin in Commun. Math. Phys. 279:187–223, [2008]) the standard DLA model from (Witten and Sander in Phys. Rev. B 27:5686–5697, [1983]) was considered on a cylinder and the arm growing phenomena was established, provided that the section of the cylinder has sufficiently fast mixing rate. When considering DLA on a cylinder it is natural to ask how many particles it takes to clog the cylinder, e.g. modeling clogging of arteries. In this note we formulate a very simple DLA clogging model and establish an exponential lower bound on the number of particles arriving before clogging appears. In particular we possibly shed some light on why it takes so long to reach the bypass operation.