Random.

Summary The texts in this volume present several aspects of the mathematics of randomness and highlight the many fields of application in which they are used. Sylvie Méléard uses population dynamics modeling to introduce Markovian jump processes. She highlights, through the study of large population approximations of the logistic birth and death process, an ordinary differential equation model and a stochastic differential equation model, depending on the time scale and population size considered. Christophe Giraud provides an introduction to the mathematical foundations of automatic classification, a theory that is used both in the filtering of email spam and in the automatic search for active molecules in medicine. His text presents various mathematical techniques used in the estimation of the probability of classification error by an algorithm. Djalil Chafaï develops some aspects of the theory of random matrices, which is a field of mathematics at the intersection of probability theory and linear algebra. This theory has applications in applied fields as well as in the most fundamental parts of mathematics.