18th of December 2015
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Next Mark Kac seminar
||6th of October 2017 tot 1st of October 2017
Friday October 6
Utrecht, Janskerkhof 15a, room 001 (morning) and 101 (afternoon)
Speaker: Raphael Cerf (Orsay)
Title : Quasispecies and error threshold for a finite population
Speaker: Conrado Da Costa (Leiden)
Title : On the strong law of Large Numbers for the Random Walk
in the Cooling Random Environment
Abstract Raphael Cerf
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.
Abstract Conrado Da Costa
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.
The Mark Kac seminar is supported by FOM and is an activity of the STAR
stochastics cluster. See also our website http://www.win.tue.nl/markkac
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