On the structure of random graphs with constant \(r\)-balls

DOI10.4171/JEMS/1181MaRDI QIDQ2693149

Itai Benjamini, David Ellis

Publication date: 17 March 2023

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.02002

zbMATH Keywords

polynomial growthautomorphism grouprandom graphsconnectivity

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Enumeration in graph theory (05C30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Distance in graphs (05C12) Other geometric groups, including crystallographic groups (20H15) Connectivity (05C40)

Cites Work

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• On the phase transition in random simplicial complexes
• Coarse geometry and randomness. École d'Été de Probabilités de Saint-Flour XLI -- 2011
• Random Latin squares and 2-dimensional expanders
• Automorphisms of random graphs with specified vertices
• Homological connectivity of random 2-complexes
• Volumes of symmetric spaces via lattice points
• Nonpositively curved manifolds of higher rank
• Manifolds of nonpositive curvature and their buildings
• Ramanujan graphs
• The isoperimetric number of random regular graphs
• A probabilistic proof of an asymptotic formula for the number of labelled regular graphs
• Explicit Tauberian estimates for functions with positive coefficients
• A method and two algorithms on the theory of partitions
• The size of bipartite graphs with a given girth
• Uniform infinite planar triangulations
• Locally grid graphs: Classification and Tutte uniqueness
• Recurrence of distributional limits of finite planar graphs
• Subgroup growth.
• Collapsibility and vanishing of top homology in random simplicial complexes
• Recurrence of planar graph limits
• On covers of graphs by Cayley graphs
• On dice and coins: Models of computation for random generation
• The topological structure of scaling limits of large planar maps
• Local-to-global rigidity of Bruhat-Tits buildings
• The distribution of the number of summands in the partitions of a positive integer
• Integer multiplication in time \(O(n\log n)\)
• The threshold for d-collapsibility in random complexes*
• ON THE STRUCTURE OF GRAPHS WHICH ARE LOCALLY INDISTINGUISHABLE FROM A LATTICE
• Residual Properties of Infinite Soluble Groups
• A Census of Planar Triangulations
• Crystallography and Cohomology of Groups
• The Structure of Random Partitions of Large Integers
• A new series of dense graphs of high girth
• The Asymptotic Number of Unlabelled Regular Graphs
• Characterizing a vertex‐transitive graph by a large ball
• HIGH DIMENSIONAL EXPANDERS
• When does the top homology of a random simplicial complex vanish?
• Random geometry on the sphere
• On the enumeration of planar maps
• Tilings of the Torus and the Klein Bottle and Vertex-Transitive Graphs on a Fixed Surface
• A General Asymptotic Formula for Partition Functions
• Some Theorems on Abstract Graphs
• On Infinite Soluble Groups (III)

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