diff options
-rwxr-xr-x | header.tex | 2 | ||||
-rwxr-xr-x | main.tex | 13 |
2 files changed, 14 insertions, 1 deletions
@@ -65,7 +65,7 @@ % Layout % \usefonttheme[onlymath]{serif} -\usefonttheme[stillsansseriflarge]{serif} +\usefonttheme[stillsansseriflarge,stillsansserifsmall]{serif} % \useinnertheme{rounded} \usecolortheme{seahorse} \usecolortheme{orchid} @@ -58,6 +58,7 @@ \begin{frame} {Some references} \begin{itemize} + \itemsep.2cm \item \fullcite{MR3509213} \item \fullcite{pavliotis2011applied} \item Lecture notes by Gabriel Stoltz on computational statistical physics: @@ -108,6 +109,7 @@ \[ \rho = \int_{0}^{\infty} \expect_{\mu} \bigl[\varphi(x_t) \phi(x_0)\bigr] \, \d t. \] + We will derive this formula from linear response. \item Transient techniques: \end{itemize} @@ -136,6 +138,17 @@ \end{theorem} \end{frame} +\begin{frame} + {Existence of an invariant measure for noneq.\ dynamics} + Consider the paradigmatic dynamics + \begin{align*} + \d q_t &= M^{-1} p_t \, \d t, \\ + \d p_t &= - \bigl(\grad V(q_t) + \eta F\bigr) \, \d t - \gamma M^{-1} p_t \, \d t + \sqrt{\frac{2 \gamma}{\beta}} \, \d W_t, + \end{align*} + where $(q_t, p_t) = \torus^d \times \real^d$ and $F \in \real^d$ with $\abs{F} = 1$ is a given direction. + +\end{frame} + \end{document} % vim: ts=2 sw=2 |