Timeline for Probability of return at step $n$ of a Random walk to its starting vertex
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Mar 28, 2011 at 14:32 | vote | accept | Chris | ||
| Mar 27, 2011 at 13:38 | comment | added | Did | You are welcome. Re your comment to @Ben, omitting aperiodicity conditions, on finite graphs the situation is similar to what I describe for $\mathbb{Z}/N\mathbb{Z}$ with $N$ odd. Namely, $p^{(n)}_{00}(G)\to\pi_G(0)$ where $\pi_G$ denotes the stationary probability distribution of the simple random walk on $G$. Hence, for each vertex $x$ of $G$, $\pi_G(x)$ is the degree of $x$ divided by the sum of the degrees of all the vertices of $G$. | |
| Mar 27, 2011 at 10:37 | comment | added | Chris | Didier: thanks! This is exactly the information I was hoping for. Are there maybe similar formulas for other finite graphs? FYI: As reference for your formula I found Eq.4 in S. Chandrasekhar, "Stochastic Problems in Physics and Astronomy". | |
| Mar 26, 2011 at 19:41 | history | undeleted | Did | ||
| Mar 26, 2011 at 16:35 | history | deleted | Did | ||
| Mar 26, 2011 at 16:29 | history | edited | Did | CC BY-SA 2.5 |
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| Mar 26, 2011 at 16:22 | history | answered | Did | CC BY-SA 2.5 |