Trees with power-like height dependent weight
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Trees with power-like height dependent weight. / Durhuus, Bergfinnur; Ünel, Meltem.
In: Electronic Journal of Probability, Vol. 27, 137, 2022.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Trees with power-like height dependent weight
AU - Durhuus, Bergfinnur
AU - Ünel, Meltem
N1 - Publisher Copyright: © 2022, Institute of Mathematical Statistics. All rights reserved.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - height coupled trees
KW - local limits of BGW trees
KW - random trees
UR - http://www.scopus.com/inward/record.url?scp=85139426774&partnerID=8YFLogxK
U2 - 10.1214/22-EJP857
DO - 10.1214/22-EJP857
M3 - Journal article
AN - SCOPUS:85139426774
VL - 27
JO - Electronic Journal of Probability
JF - Electronic Journal of Probability
SN - 1083-6489
M1 - 137
ER -
ID: 330404464