All Questions
8 questions
11
votes
1
answer
435
views
(almost) statistical independence of nodes degrees in a graph
Wireless networks are typically modeled as random geometric graphs. The number of nodes $N$ in the network is drawn from a Poisson distribution with intensity $\lambda$
$$P(N = n) = \frac{\lambda^n ...
- 241
5
votes
1
answer
222
views
Switching oriented paths in a graph
Consider an oriented graph (e.g. a finite part of the standard grid with some random orientations).
Each minute the following operation takes place: we choose uniformly randomly an ordered pair $(A,B)...
- 5,063
5
votes
0
answers
136
views
What's the variance in the Six Degrees model?
Recall the six degrees of Kevin Bacon game. You can even play the game at The Oracle of Bacon, and their search works via Breadth First Search.
I interpret the punchline as saying that if I start ...
- 30.3k
3
votes
0
answers
98
views
Asymptotic results on statistical graph models
This post is partly inspired by this post.
Reference request: results on the asymptotic distribution of singular values related to a random orthogonal matrix
While it is well-known that two basic ...
- 8,071
2
votes
1
answer
165
views
Is a random $(r+1,r)$-biregular bipartite graph $r$-edge connected w.h.p?
A uniformly random $r$-regular bipartite graph on $n$ vertices is known to be $r$-edge connected. That is, with high probability as $n$ grows large, the minimum size of a cut in a random $r$-regular ...
- 153
2
votes
1
answer
160
views
Do product distributions (or graph products) eventually cluster as more products are taken?
Say we have a joint distribution on a finite alphabet $\mathcal{X}\times \mathcal{Y}$. It could be a communication link where we want to send a random message $X$ over a channel, but it gets garbled ...
1
vote
0
answers
45
views
What is the number of iterations needed for the message passing algorithm to converge when applied to an acyclic factor graph?
I understand that the message passing algorithm (Belief Propagation algorithm), when applied to a factor graph consists in an exchange in messages between the factor nodes and the variable nodes, ...
- 39
0
votes
1
answer
77
views
Fourth moment of a random-variable with block-tridiagonal structure
Let x be a random variable in $\mathbb{R}^d$, $J$ a block tridiagonal $d\times d$ matrix, and probability of $x$ is defined as follows
$$p(x)\propto \exp(-x'Jx)$$
For a fixed $d\times d$ matrix $v$ ...
- 2,252