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Activity Number: 122
Type: Contributed
Date/Time: Monday, August 1, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Physical and Engineering Sciences
Abstract #318663 View Presentation
Title: Degree Profile of Hierarchical Lattice Networks
Author(s): Yarong Feng* and Hosam Mahmoud and Ludger Ruschendorf
Companies: The George Washington University and The George Washington University and Albert-Ludwigs University of Freiburg
Keywords: random graph ; contraction method ; Wasserstein distance ; phase transition ; recurrence ; Network

We study the degree profile of random hierarchical lattice networks. At every step, each edge is either serialized (with probability p) or parallelized (with probability 1 ? p). We establish an asymptotic Gaussian law for the number of nodes of outdegree 1, and show how to extend the derivations to encompass asymptotic limit laws for higher outdegrees. The asymptotic joint distribution of the number of nodes of outdegree 1 and 2 is shown to be bivariate normal. No phase transition with p is detected in these asymptotic laws.

For the limit laws, we use ideas from the contraction method. The recursive equations which we get involves coefficients and toll terms depending on the recursion variable and thus are not in the standard form of the contraction method. Yet, an adaptation of the contraction method goes through, showing that the method has promise for a wider range of random structures and algorithms.

Authors who are presenting talks have a * after their name.

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