A moment-generating formula for Erdős-Rényi component sizes
نویسندگان
چکیده
منابع مشابه
Concentration of the Kirchhoff index for Erdős-Rényi graphs
Given an undirected graph, the resistance distance between two nodes is the resistance one would measure between these two nodes in an electrical network if edges were resistors. Summing these distances over all pairs of nodes yields the so-called Kirchhoff index of the graph, which measures its overall connectivity. In this work, we consider Erdős-Rényi random graphs. Since the graphs are rand...
متن کاملErdős - Rényi Random Graphs + Forest Fires = Self - Organized Criticality
We modify the usual Erd˝ os-Rényi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the intensity of rate of lightnings the system sticks to a permanent critical state. The authors thank the anonymous referee for thoroughly reading the manuscript. Her/his comments and suggestions hel...
متن کاملErdős-Rényi Sequences and Deterministic Construction of Expanding Cayley Graphs
Given a finite group G by its multiplication table as input, we give a deterministic polynomial-time construction of a directed Cayley graph on G with O(log |G|) generators, which has a rapid mixing property and a constant spectral expansion. We prove a similar result in the undirected case, and give a new deterministic polynomialtime construction of an expanding Cayley graph with O(log |G|) ge...
متن کاملExplosive Percolation in Erdős-Rényi-Like Random Graph Processes
The evolution of the largest component has been studied intensely in a variety of random graph processes, starting in 1960 with the Erdős-Rényi process (ER). It is well known that this process undergoes a phase transition at n/2 edges when, asymptotically almost surely, a linear-sized component appears. Moreover, this phase transition is continuous, i.e., in the limit the function f(c) denoting...
متن کاملFirst Passage Percolation on the Erdős-Rényi Random Graph
In this paper we explore first passage percolation (FPP) on the Erdős-Rényi random graph Gn(pn), where each edge is given an independent exponential edge weight with rate 1. In the sparse regime, i.e., when npn → λ > 1, we find refined asymptotics both for the minimal weight of the path between uniformly chosen vertices in the giant component, as well as for the hopcount (i.e., the number of ed...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2018
ISSN: 1083-589X
DOI: 10.1214/18-ecp126