 
Summary: A simole model for DLA
M.Anshelevich
Pr. Nikolai Makarov
Abstract
A very simple model of a growing aggregate is considered. It is governed by a
parameter 11, and it turns out that for 11< = 1 the system grows uniformly while for 11> 1
the system grows almost exclusively in one direction.
Introduction
Consider the following model: we have N parallel sticks of integer length, and at
integer moments exactly one stick grows by 1, with the probability of kth stick growing
proportional to a fixed power 1'1of its length, properly normalized. Equivalently, we
consider sequences of points of the first quadrant of Rn such that on each step exactly one
of the coordinates of the point gets incremented by 1, and the probability of kth
coordinate being incremented is
11
(1) r?
LX~
k=1
The behavior of the system depends on the value of 11,specifically it is different for
11>1,11=1,11<1.
