Peter
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 Feb 29 awarded Yearling Feb 29 accepted How do you “linearize” a differential operator to get its symbol? Feb 29 asked How do you “linearize” a differential operator to get its symbol? Jan 10 asked Inequality in the proof of a LDP for the largest eigenvalue of the GOE Nov 26 revised Eliminating correlation by change of variables (on a sphere) added my take on the problem Nov 26 asked Eliminating correlation by change of variables (on a sphere) May 4 comment Finding the matrix representation of a linear transformation $T: P_{3} \to \text{M}_{2 \times 2}$. By linearity it suffices to check what $T$ does to the basis elements, how about calculating $T(1), T(x),T(x^2),T(x^3)$ and writing it as a linear combination of those? ($T(a_0+a_1x+\dots)=a_0T(1)+a_1T(x)+\dots$) Jan 18 awarded Tumbleweed Jan 14 accepted How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators Jan 14 comment How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators Ahh, that explains quite a lot, now (at least in 1D, but that's enough to convince me for now) it reduces to $e^{-\beta U}\mathcal{L}^* g$! Do you want to post this as an answer so I can mark this question as answered? Jan 13 revised How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators added case in 1D Jan 13 revised How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators suggested approach Jan 13 comment How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators Yes, we are. That's just what I tried, but I'm stuck with said term (added it in the question) and I don't see a way to rescue this ansatz, so I wanted to ask if there'd be a more sophisticated approach. Jan 13 revised How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators added my current progress Jan 13 asked How to prove $\mathcal{L}e^{-U}g = e^{-U}\mathcal{L}^*g$ for Fokker-Planck operators Dec 13 awarded Citizen Patrol Sep 24 awarded Autobiographer Sep 21 comment What can I think of the function $F$ that's being used for most(?) explicit first order ODEs? @"Are there any such sentences in the book? Did the professor say anything at all while writing those formulas?" There aren't any explanations in the book and I couldn't attend the lecture (as well as multivariate calculus which might explain the above problem) because I had to do alternative service. Maybe he said something in the lectures, but my fellow students didn't have a clue either. Sep 21 comment What can I think of the function $F$ that's being used for most(?) explicit first order ODEs? Thank you very much! Finally I have an idea of what $F$ looks like! The last equation makes perfectly sense now and the second last the problem reduced to the question why there's an $F$ after $\frac{\Delta F}{\Delta y}$ and not after $\frac{\Delta F}{\Delta t}$, but I guess this has something to do with $y$ being a vector. However, this is not part of the original question anymore. Sep 21 accepted What can I think of the function $F$ that's being used for most(?) explicit first order ODEs?