Three series of lectures were given at the 34th Probability Summer School in Saint-Flour (July 6 24, 2004), by the Professors Cerf, Lyons and Slade. We have decided to publish these courses separately. This volume contains the course of Professor Cerf. We cordially thank the author for his performance at the summer school, and for the redaction of these notes. 69 participants have attended this school. 35 of them have given a short lecture. The lists of participants and of short lectures are enclosed at the end of the volume. The Saint-Flour Probability Summer School was founded in 1971. Here...
Three series of lectures were given at the 34th Probability Summer School in Saint-Flour (July 6 24, 2004), by the Professors Cerf, Lyons and Slade. W...
The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. The author considers a Moran model describing the evolution of a population of size m of chromosomes of length over an alphabet of cardinality . The mutation probability per locus is q. He deals only with the sharp peak landscape: the replication rate is >1 for the master sequence and 1 for the other sequences. He studies the equilibrium distribution of the process in the regime where ,m ,q 0, q a ]0, [,m [0, ].
The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. The author considers a Mo...
