Scaling Limits of Random Graphs from Subcritical Classes

@article{Panagiotou2014ScalingLO,
  title={Scaling Limits of Random Graphs from Subcritical Classes},
  author={Konstantinos Panagiotou and Benedikt Stufler and Kerstin Weller},
  journal={arXiv: Probability},
  year={2014}
}
We study the uniform random graph $\mathsf{C}_n$ with $n$ vertices drawn from a subcritical class of connected graphs. Our main result is that the rescaled graph $\mathsf{C}_n / \sqrt{n}$ converges to the Brownian Continuum Random Tree $\mathcal{T}_{\mathsf{e}}$ multiplied by a constant scaling factor that depends on the class under consideration. In addition, we provide subgaussian tail bounds for the diameter $\text{D}(\mathsf{C}_n)$ and height $\text{H}(\mathsf{C}_n^\bullet)$ of the rooted… Expand

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