  Sampling from distributions play a crucial role in aiding practitioners with
statistical inference. However, in numerous situations, obtaining exact samples
from complex distributions is infeasible. Consequently, researchers often turn
to approximate sampling techniques to address this challenge. Fast approximate
sampling from complicated distributions has gained much traction in the last
few years with considerable progress in this field. Previous work has shown
that for some problems a preconditioning can make the algorithm faster. In our
research, we explore the Langevin Monte Carlo (LMC) algorithm and demonstrate
its effectiveness in enabling inference from the obtained samples.
Additionally, we establish a convergence rate for the LMC Markov chain in total
variation. Lastly, we derive non-asymptotic bounds for approximate sampling
from specific target distributions in the Wasserstein distance, particularly
when the preconditioning is spatially invariant.
