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Results tagged with random-graphs
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user 11260
The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.
6
votes
Accepted
Citations graphs: what is known?
A great deal is known about citation graphs. For example, an analysis of the citation graph for the computer science literature answers the three questions in the OP as:
• the connected component has …
- 188k
1
vote
Accepted
Are the eigenvalues of the 1D lattice with random weights known?
I presume this will depend on the connectivity of the 1D lattice. Let me consider the simple case of nearest neighbor connections, when the adjacency matrix $A$ is tridiagonal with the same values on …
- 188k
4
votes
Good broad review of agent-based modeling?
This is just out (April 2015): An Introduction to Agent-Based Modeling
Agent-based modeling attempts to understand natural and social
phenomena by recreating them in computer
simulations,
sh …
- 188k
2
votes
Accepted
Figuring out a consistent definition for the percolation backbone
source
Both striped sites and black sites belong to the percolation cluster, but only the black sites are part of the backbone. The backbone can be defined as the set of current carrying paths from …
- 188k
4
votes
Accepted
Electrode assignment problem in resistive networks
Best practice to determine the resistivity tensor is to use the van der Pauw method. For resistor networks this method is used for example in Nonlinearity of resistive impurity effects on van der Pauw …
- 188k
1
vote
Limit of normalized sum of Dirac measures at first $\lfloor p/2\rfloor$ eigenvalues of the s...
Let me denote the Marcenko-Pastur distribution by $\rho(\lambda)$, so that $\rho(\lambda)d\lambda$ gives the probability for an eigenvalue to be in the interval $(\lambda,\lambda+d\lambda)$, in the li …
- 188k
7
votes
Accepted
(Asymmetric) matrix power series in closed form: $\sum_{i=0}^{\infty} A^i \left(A^i\right)^{...
Let me answer the first question:
Q: Does $F=\sum_{i=0}^{\infty} A^i (A^i)^{\top}$ for non-symmetric $A$ have a closed-form solution analogous to the solution $\sum_{i=0}^{\infty} A^{2i}=\left( I-A^2 …
- 188k
1
vote
Sources of information on algorithms for finding Hamiltonian cycles (Pósa)
See A Brief Introduction to Hamilton Cycles in Random Graphs for an introductory overview, and arXiv:1901.07139 for an annotated biography.
- 188k