Processos de partÃculas sem colisÃes

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

We consider a class of particle processes with discrete time and a finite number of types of particles, which we call Processes Without Collisions or PWC for short. At every time step, any particle may die or transform itself into one or several particles of any types with certain probabilities, but there are no collisions, that is, every transformation applies to only one particle and its probability does not depend on the other particles. This excludes predator-prey and sexual relations, but includes death and asexual reproduction with possible mutations. Due to this restriction, positions of particles are irrelevant and we do not mention them. We prove that if the number of particles tends to infinity, the behavior of the process becomes deterministic after normalization. In fact, this approximation is often used without a proper foundation. We also prove that the resulting dynamic system has a fixed point and that under additional conditions the fixed point is unique and the system tends to it from any initial condition. Besides, this approach raises some questions about the manner in which some books on populational dynamics are written

ASSUNTO(S)

processos de ramificaÃÃo particle systems probabilidade branching processes probability sistemas de partÃculas matematica da computacao

ACESSO AO ARTIGO

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