2023/08/09 by Kiran R. Bhutani, Ravi Kalpathy, Hosam M. Mahmoud
Mathematics · #Markov Chains and Monte Carlo Methods #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.32408/compositionality-5-6
The theme in this paper is a composition of random graphs and P'olya urns. The random graphs are generated through a small structure called the seed. Via P'olya urns, we study the asymptotic degree structure in a random m-ary hooking network and identify strong laws. We further upgrade the result to second-order asymptotics in the form of multivariate Gaussian limit laws. We give a few concrete examples and explore some properties with a full representation of the Gaussian limit in each case. The asymptotic covariance matrix associated with the P'olya urn is obtained by a new method that originated in this paper and is reported in [25].