Abstract
The main substance of the paper concerns growth rate and classification (ergodicity, transience) of a family of random trees. In the basic model new edges appear according to a Poisson process of parameter A and leaves can be deleted at a rate μ. The main results lay the stress on the famous number e. A complete classification of the process is given in terms of the intensity factor ρ=λ/μ: it is ergodic if ρ ≤ e−1and transient if ρ > e−1. There is a phase transition phenomenon: the usual region of null recurrence (in the parameter space) here does not exist. This fact is rare for countable Markov chains with exponentially distributed jumps A theorem, much of ergodic type is derived for the height of the tree at time t, which in the transient case is shown to grow linearly as t → ∞, at a rate explicitly computed.
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Fayolle, G., Krikun, M. (2002). Growth Rate and Ergodicity Conditions for a Class of Random Trees. In: Chauvin, B., Flajolet, P., Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science II. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8211-8_23
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DOI: https://doi.org/10.1007/978-3-0348-8211-8_23
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9475-3
Online ISBN: 978-3-0348-8211-8
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