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RANDOM GRAPHS WITH A GIVEN DEGREE SEQUENCE。
Induced subgraphs in sparse random graphs with given degree sequence
Induced subgraphs math
2010/11/22
For any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is a given graph $H$ on the vertex set $S$. The result holds for any $d=o(n^{1/3})$ and is fu...
Spectral distributions of adjacency and Laplacian matrices of random graphs
Spectral distributions Laplacian matrices random graphs
2010/11/18
In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest ...
A probabilistic approach to local limit theorems with applications to random graphs
local limit theorems applications to random graphs
2010/11/19
In this article, we develop a general method to obtain local limit theorems from distributional limit theorems. Our results use probabilistic arguments and yield explicit bounds on the quality of app...
A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show i...