Poisson convergence and Poisson processes with applications to random graphs

DOI10.1016/0304-4149(87)90048-2zbMath0633.60070OpenAlexW2086188621MaRDI QIDQ1096252

Svante Janson

Publication date: 1987

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(87)90048-2

zbMATH Keywords

Stein-Chen methodrandom graph theoryconvergence of weakly dependent point processes to a Poisson point processgraph with a large number of vertices

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Paths and cycles (05C38) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items

Cycles in a Uniform Graph Process, Smooth and sharp thresholds for random{k}-XOR-CNF satisfiability, Smooth and sharp thresholds for random{k}-XOR-CNF satisfiability, Combinatorial sharpness criterion and phase transition classification for random CSPs, Threshold functions for small subgraphs: an analytic approach, Multicyclic components in a random graph process, Counting graceful labelings of trees: a theoretical and empirical study, Cores of random \(r\)-partite hypergraphs, First cycles in random directed graph processes, The first cycles in an evolving graph, Thresholds for classes of intersection graphs, The scaling limit of Poisson-driven order statistics with applications in geometric probability, Homomorphism complexes and \(k\)-cores, A note on mixed Poisson approximation, A counterexample to the DeMarco‐Kahn upper tail conjecture, A central limit theorem for decomposable random variables with applications to random graphs, Multiscale dynamics of an adaptive catalytic network, The Janson inequalities for general up‐sets, Implicit consensus clustering from multiple graphs, On the Distribution of Monochromatic Complete Subgraphs and Arithmetic Progressions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Limit theorems for a triangular scheme of U-statistics with applications to inter-point distances
• A Poisson limit theorem for incomplete symmetric statistics
• Random trees in a graph and trees in a random graph
• A Poisson limit theorem for weakly exchangeable events
• Poisson convergence and random graphs
• Dissociated random variables
• Two central limit problems for dependent random variables
• Short distances, flat triangles and Poisson limits
• Poisson approximation for some statistics based on exchangeable trials