The field of stochastic differential equations and sampling algorithms is witnessing significant developments, with a focus on improving the stability and accuracy of numerical methods. Researchers are exploring innovative techniques to tackle the challenges posed by superlinear drifts and non-log-concave distributions. One notable direction is the development of modified tamed schemes, which aim to balance the trade-off between accuracy and stability. Another area of interest is the analysis of mixing times for Glauber dynamics, with recent results providing improved estimates for monotone systems. Furthermore, advancements in sampling algorithms are being made, including the development of new methods for non-log-concave distributions and the improvement of existing algorithms for log-concave distributions. Noteworthy papers in this area include:

• A modified tamed scheme for stochastic differential equations with superlinear drifts, which introduces an additional cut-off function to improve accuracy and stability.
• Improved sampling algorithms and Poincaré inequalities for non-log-concave distributions, which show that a moderate strengthening of the smoothness condition can lead to an exponential gap in query complexity.
• Analysis of Langevin midpoint methods using an anticipative Girsanov theorem, which provides improved regularity and cross-regularity results for sampling methods.