Trees with power-like height dependent weight
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We consider planar rooted random trees whose distribution is even for fixed height h and size N and whose height dependence is given by a power function hα. Defining the total weight for such trees of fixed size to be ZN, a detailed analysis of the analyticity properties of the corresponding generating function is provided. Based on this, we determine the asymptotic form of ZN and show that the local limit at large size is identical to the Uniform Infinite Planar Tree, independent of the exponent α of the height distribution function.
Originalsprog | Engelsk |
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Artikelnummer | 137 |
Tidsskrift | Electronic Journal of Probability |
Vol/bind | 27 |
Antal sider | 24 |
ISSN | 1083-6489 |
DOI | |
Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
*Supported by Villum Fonden via the QMATH Centre of Excellence (Grant no. 10059). †University of Copenhagen, Denmark. E-mail: durhuus@math.ku.dk ‡University of Copenhagen, Denmark. E-mail: meltem@math.ku.dk
Publisher Copyright:
© 2022, Institute of Mathematical Statistics. All rights reserved.
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