The order of the giant component of random hypergraphs
نویسندگان
چکیده
We establish central and local limit theorems for the number of vertices in the largest component of a random d-uniform hypergraph Hd(n, p) with edge probability p = c/ ( n−1 d−1 ) , where (d − 1) + ε < c < ∞. The proof relies on a new, purely probabilistic approach, and is based on Stein’s method as well as exposing the edges of Hd(n, p) in several rounds.
منابع مشابه
Critical Random Hypergraphs: the Emergence of a Giant Set of Identifiable Vertices
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase transition takes various forms, depending on the values of the parameters controlling the different types of hyperedges. It may be continuous as in a random graph (...
متن کاملEvolution of high-order connected components in random hypergraphs
We consider high-order connectivity in k-uniform hypergraphs defined as follows: Two j-sets are j-connected if there is a walk of edges between them such that two consecutive edges intersect in at least j vertices. We describe the evolution of jconnected components in the k-uniform binomial random hypergraph H(n, p). In particular, we determine the asymptotic size of the giant component shortly...
متن کاملCritical Random Hypergraphs: the Emergence of a Giant Set of Identifiable Vertices by Christina Goldschmidt
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase transition takes various forms, depending on the values of the parameters controlling the different types of hyperedges. It may be continuous as in a random graph. ...
متن کاملStochastical models for networks in the life sciences
Motivated by structural properties of molecular similarity networks we study the behaviour of the component evolution in two different stochastic network models, that is random hypergraphs and random intersection graphs. We prove gaussian distribution for the number of vertices in the giant component of a random d-uniform hypergraph (a local limit theorem in the Hd(n, p) model for p = c/ (n−1 d...
متن کاملHigh-order Phase Transition in Random Hypergrpahs
In this paper, we study the high-order phase transition in random r-uniform hypergraphs. For a positive integer n and a real p ∈ [0, 1], let H := H(n, p) be the random r-uniform hypergraph on the vertex set [n], where each r-set is an edge with probability p independently. For 1 ≤ s ≤ r − 1 and two s-sets S and S, we say S is connected to S if there is a sequence of alternating s-sets and edges...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Random Struct. Algorithms
دوره 36 شماره
صفحات -
تاریخ انتشار 2010