BETANCOURT ET AL. c2nomgameaahn极afmahoot I(Langevin wi T(Langevin with 10) (a) (b) (e) al point. en here for a Langevin diffusion targeting the tisted Gaussian distrib tion (Haario,Saksman and Tamminen,2001).8 BETANCOURT ET AL. Fig 2. Langevin trajectories are, by construction, diffusive, and are just as likely to double back as they are to move forward. Consequently even as the diffusion time grows, here to t = 1000 as the trajectory darkens, realizations of a Langevin diffusion targeting the twisted Gaussian distribu￾tion (Haario, Saksman and Tamminen, 2001) only slowly wander away from the initial point. δq0 T (Langevin with t=1) (a) δq0 T (Langevin with t=10) (b) δq0 T (Langevin with t=100) (c) Fig 3. Because of the diffusive nature of the underlying maps, Langevin kernels expand very slowly with increasing diffusion time, t. For any reasonable diffusion time the resulting kernels will concentrate around the initial point, as seen here for a Langevin diffusion targeting the twisted Gaussian distribu￾tion (Haario, Saksman and Tamminen, 2001)