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On the stability of file-sharing systems

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Stochastic Processes in Communication Sciences

In a recent paper of Eichelsbacher and K{“o}nig (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a $k$-dimensional random walk conditioned to stay in a strict order at all times. Moreover, they have shown that the rescaled random walk converges to the Dyson Brownian motion. In the present paper we find the optimal moment assumptions for the construction of the conditional random walk and generalise the limit theorem for this conditional process.

This talk is part of the Isaac Newton Institute Seminar Series series.

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