Precise logarithmic asymptotics for the right tails of some limit random variables for random trees
2009 (English)In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 12, no 4, 403-416 p.Article in journal (Refereed) Published
For certain random variables that arise as limits of functionals of random finite trees, we obtain precise asymptotics for the logarithm of the right-hand tail. Our results are based on the facts (i) that the random variables we study can be represented as functionals of a Brownian excursion and (ii) that a large deviation principle with good rate function is known explicitly for Brownian excursion. Examples include limit distributions of the total path length and of the Wiener index in conditioned Galton-Watson trees (also known as simply generated trees). In the case of Wiener index (where we recover results proved by Svante Janson and Philippe Chassaing by a different method) and for some other examples, a key constant is expressed as the solution to a certain optimization problem, but the constant's precise value remains unknown.
Place, publisher, year, edition, pages
2009. Vol. 12, no 4, 403-416 p.
large deviations, tail asymptotics, Galton-Watson trees, simply generated families of trees, Brownian excursion, variational problems, total path length, Wiener index
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-114319DOI: 10.1007/s00026-009-0006-0ISI: 000264809400004OAI: oai:DiVA.org:uu-114319DiVA: diva2:293727