Rate of Convergence to the Poisson Law of the Numbers of Cycles in the Generalized Random Graphs

DOI10.1007/978-3-030-76829-4_5zbMath1486.05274arXiv2101.06431OpenAlexW3207353010MaRDI QIDQ5014516

Maria A. Danshina, Sergey G. Bobkov, Vladimir V. Ulyanov

Publication date: 8 December 2021

Published in: Operator Theory and Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.06431

zbMATH Keywords

rate of convergencecyclesPoisson lawgeneralized random graphs

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Probability distributions: general theory (60E05) Enumeration in graph theory (05C30)

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Cites Work

• Unnamed Item
• Central limit type theorems in the generalized random graphs with random vertex weights
• Novel scaling limits for critical inhomogeneous random graphs
• Generating simple random graphs with prescribed degree distribution
• Two moments suffice for Poisson approximations: The Chen-Stein method
• Relaxing the uniformity and independence assumptions using the concept of fractal dimension
• Poisson approximation and the Chen-Stein method. With comments and a rejoinder by the authors
• Connected components in random graphs with given expected degree sequences
• Upper tails for subgraph counts in random graphs
• Limit laws for the number of triangles in the generalized random graphs with random node weights
• Random Graphs and Complex Networks
• Upper tails for triangles
• Asymptotic equivalence and contiguity of some random graphs
• The Volume of the Giant Component of a Random Graph with Given Expected Degrees
• Divide and conquer martingales and the number of triangles in a random graph
• The phase transition in inhomogeneous random graphs
• On a conditionally Poissonian graph process
• Random Graphs