## October 6, 2017

Location: Janskerkhof 15a (Utrecht), room 001 (morning) and 101 (afternoon)

In 1971, Manfred Eigen designed a model to understand the evolution of a population of macromolecules, driven by mutation and selection. A fundamental discovery of Eigen is the existence of an error threshold for the mutation rate. Above this threshold, the population becomes completely random. Below this threshold, a quasispecies is formed around the most fit macromolecule. However, the Eigen model deals with an infinite population. We will show how the notions of error threshold and quasispecies can be formulated in the classical models of population genetics dealing with finite populations. We will also give exact formulas for the quasispecies distribution.

### On the strong law of Large Numbers for the Random Walk in the Cooling Random Environment

Random Walks in Dynamical random environment consist of a type of random walk whose transition rules depend on the time and the position of the walker. We consider in this talk a specific kind of Dynamic random environment, the Cooling random environment, as introduced in the paper “Random walks in cooling random environments” by Avena and den Hollander. The goal of the talk is to discuss the basic ideas and tools used in the proof of the Strong Law of Large Numbers for the Random Walk in the Cooling Random Environment.