Silvia Businger - Asymptotics of the occupancy scheme in a random environment and its applications to tries

dmtcs:2037 - Discrete Mathematics & Theoretical Computer Science, August 4, 2017, Vol. 19 no. 1 - https://doi.org/10.23638/DMTCS-19-1-22
Asymptotics of the occupancy scheme in a random environment and its applications to triesArticle

Authors: Silvia Businger

    Consider $ m $ copies of an irreducible, aperiodic Markov chain $ Y $ taking values in a finite state space. The asymptotics as $ m $ tends to infinity, of the first time from which on the trajectories of the $ m $ copies differ, have been studied by Szpankowski (1991) in the setting of tries. We use a different approach and model the $ m $ trajectories by a variant of the occupancy scheme, where we consider a nested sequence of boxes. This approach will enable us to extend the result to the case when the transition probabilities are random. We moreover use the same techniques to study the asymptotics as $ m $ tends to infinity of the time up to which we have observed all the possible trajectories of $ Y $ in random and nonrandom scenery.


    Volume: Vol. 19 no. 1
    Section: Analysis of Algorithms
    Published on: August 4, 2017
    Accepted on: July 26, 2017
    Submitted on: August 4, 2017
    Keywords: Mathematics - Probability,60F10, 60J10, 60J80

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