# Tony Lelièvre: Mini-course - Sampling problems in computational statistical physics (Lecture 2)

Lecture 2 of 3

**Time: **
Tue 2021-01-19 15.15 - 16.15

**Lecturer: **
Tony Lelièvre, École des Ponts ParisTech

**Location: **
Zoom, meeting ID: 633 8972 2507

### Abstract

Computational statistical physics is typically a domain where efficient sampling methods are crucial. The objective is indeed to obtain macroscopic properties of materials starting from a microscopic description at the molecular level, using ensemble averages (thermodynamic properties) or averages over paths (dynamical properties). Applications are numerous in very different scientific fields such as molecular biology, chemistry or materials science. The objective of these lectures will be, starting from some prototypical sampling problems raised in statistical physics, to introduce general purpose algorithms which are useful to sample multimodal distributions, rare events and metastable trajectories. More precisely, the first lecture will be devoted to free energy adaptive biasing techniques, and their analysis using entropy techniques or standard methods to prove the convergence of stochastic algorithms. In the second lecture, we will present rare event sampling techniques in order to sample reactive trajectories, namely the pieces of trajectory between metastable states. Finally, the third lecture will be devoted to a discussion of the link between metastable dynamics and jump Markov processes, using the notion of quasi-stationary distribution, and associated algorithms (accelerated dynamics methods).