| Autor: |
Keliger, Daniel, Horvath, Illes |
| Rok vydání: |
2020 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We study the asymptotic behaviour of Markov processes on large weighted Erdos-Renyi graphs where the transition rates of the vertices are only influenced by the state of their neighbours and the corresponding weight on the edges. We find the ratio of vertices being in a certain state will converge to the solution of a differential equation obtained from mean field approximation if the graph is dense enough, namely, the average degree is at least of order $N^{\frac{1}{2}+\epsilon}$. Proof for convergence in probability in the transient regime is shown. |
| Databáze: |
arXiv |
| Externí odkaz: |
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