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Results tagged with random-graphs
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user 36212
The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.
10
votes
Accepted
Question on a paper by Benjamini/Kozma/Wormald about a “well known fact”
I have no idea where the figure $n^{0.02}$ comes from. I would usually say it's well known that the maximum degree is $O(\log n)$ (actually even this is an overestimate). It's for example found in an …
- 1,687
5
votes
Accepted
Probability of a subset of Bernoulli's being all 1's
For the concrete question, it’s equivalent to asking for the cdf of the binomial distribution. This is well known.
In general, this is a very hard problem. Janson’s Inequality is not a second moment …
- 1,687
7
votes
A Modern Proof of Erdos and Renyi's 1959 Random Graph Paper?
One can also deduce the $G(n,p)$ result from the $G(n,m)$ result: one way to generate $G(n,p)$ is to choose $m$ from the binomial distribution with $\binom{n}{2}$ trials and probability $p$, then gene …
- 1,687
1
vote
Accepted
Size of minimum cut in random graph
Yes, the limit goes to $1$.
An observation: by the Chernoff bound, with (very) high probability all vertices have degree between $0.49n$ and $0.51n$, so let's assume this holds in the following.
Fir …
- 1,687