A probabilistic model for establishment of neuron polarity

The main aim of this paper is to present a simple probabilistic model for the early stage of neuron growth: the specification on an axon out of several initially similar neuntes. The model is a Markov process with competition between the growing neuntes, wherein longer objects have more chances to grow, and parameter a determines the intensity of the competition. For a > 1 the model provides results which are qualitatively similar to the experimental ones, i.e. selection of one rapidly elongating axon out of several neuntes while other less successful neuntes stop growing at some random time. Rigorous mathematical proofs are given.