Statistics Seminars: A model for a stochastic growth process with interactions
24 April 2017 14:00 in CM221
For a directed graph containing N vertices, I introduce an N-dimensional discrete time Markov chain with positive integer valued coordinates accounting for the number of particles at each vertex of the directed graph. The Markov Chain has sequential stochastic growth dynamics in which the probability of adding a new particle to a vertex is given by a reinforcement rule. Different graph based interactions and reinforcement rules change the asymptotic behaviour of the model and I will describe particular examples where the proportion of particles tend to deterministic or random quantities as time tends to infinity. Finally, I will briefly discuss how a vertex-sensitive reinforcement rule probe the condensation phenomena and analyse phase transitions relative to the shape of the growing interface.
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