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The probability of unusually large components in the near-critical Erdős-Rényi graph
Matthew Roberts
Mar 01, 2018
The largest components of the critical Erdös-Rényi graph, G(n,p) with p=1/n, have size of order n^{2/3} with high probability. We give detailed asymptotics for the probability that there is an unusually large component, i.e. of...
Unusually large components in near-critical Erdös-Rényi graphs via ballot theorems
We consider the near-critical Erdos-Rényi random graph G(n, p) and provide a new probabilistic proof of the fact that, when p is of the form p=p(n)=1/n+λ/n4/3 and A is large, {equation presented} where Cmax is the largest...
ballot theorem Brownian motion component size Random graph random walk /dk/atira/pure/subjectarea/asjc/2600/2614 name=Theoretical Computer Science /dk/atira/pure/subjectarea/asjc/2600/2613 name=Statistics and Probability /dk/atira/pure/subjectarea/asjc/1700/1703 name=Computational Theory and Mathematics /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics
The probability of unusually large components in the near-critical Erdős-Rényi graph
Matthew Roberts
Mar 01, 2018
The largest components of the critical Erdös-Rényi graph, G(n,p) with p=1/n, have size of order n^{2/3} with high probability. We give detailed asymptotics for the probability that there is an unusually large component, i.e. of...
Unusually large components in near-critical Erdös-Rényi graphs via ballot theorems
We consider the near-critical Erdos-Rényi random graph G(n, p) and provide a new probabilistic proof of the fact that, when p is of the form p=p(n)=1/n+λ/n4/3 and A is large, {equation presented} where Cmax is the largest...
ballot theorem Brownian motion component size Random graph random walk /dk/atira/pure/subjectarea/asjc/2600/2614 name=Theoretical Computer Science /dk/atira/pure/subjectarea/asjc/2600/2613 name=Statistics and Probability /dk/atira/pure/subjectarea/asjc/1700/1703 name=Computational Theory and Mathematics /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics