Générateurs de nombres aléatoires modulo un grand entier, dont l’uniformité est assurée
This thesis is about linear random number generators with a large integer modulus. It is essential to be able to check that a generator has good properties in Monte-Carlo simulation. The generator family studied here produces points that possess a well known lattice structure that can be studied to assess the uniformity of these generators. The present work is motivated by the update of the LatMRG software which studies the lattice structure of the aforementioned generators.  This thesis first presents the different types of generators the software considers. It explains how they can be used to produce random numbers and how to study their period length. It then presents equivalences between some members of this family that are used to simplify LatMRG.  It then covers the lattice structure. The thesis describes what it is and how to characterize it. It describes the characterization of the lattice structure for the considered generators. From that, it presents a few algorithms that extract information on the uniformity of generators.  At last, the thesis describes the LatMRG software. LatMRG contains both an executable program and a library. The thesis presents both their purpose and their functionalities. It describes upgrades of the software that aim to simplify its usage. Along with the software description are a few examples that serve to illustrate the flexibility and future research avenues.
random numbers lattice structure rng Monte-Carlo simulation