Timeline for Intuition/elegant reason for why Langevin diffusion converges to $\exp(-U)$?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2021 at 14:51 | comment | added | Daniel Adams | It is no surprise that the stationary distribution puts more mass around the minimisers of $U$ ( since the particle drifts towards such minimisers). | |
| Apr 26, 2021 at 4:10 | vote | accept | Linus Hamilton | ||
| Apr 24, 2021 at 8:05 | answer | added | Nawaf Bou-Rabee | timeline score: 9 | |
| Apr 24, 2021 at 7:59 | answer | added | Abhishek Halder | timeline score: 5 | |
| Apr 24, 2021 at 7:09 | history | edited | YCor | CC BY-SA 4.0 |
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| Apr 23, 2021 at 23:18 | comment | added | pupshaw | perhaps you would consider this only a case of miraculous second-order cancellation, but you can see the stationarity in a more pathwise way via Itô's formula. But I hope you get a better answer than this. | |
| Apr 23, 2021 at 20:53 | comment | added | Carlo Beenakker | The long-time limit is the equilibrium distribution, which is the Maxwell-Boltzmann distribution $e^{-U/kT}$ --- in the units you are using $kT$ equals 1. | |
| Apr 23, 2021 at 20:40 | history | asked | Linus Hamilton | CC BY-SA 4.0 |