These notes attempt to provide an elementary introduction to the one-dimensional discrete-
time branching random walk and to exploit its spinal structure. They begin with the case of …

This monograph contains the notes of lectures I gave in Saint Flour Probability Summer
School in July 2016. The two other courses were given by Paul Bourgade and by Scott …

Consider a branching random walk on the real line in the boundary case. The associated
additive martingales can be viewed as the partition function of a directed polymers on a …

Consider the supercritical branching random walk on the real line in the boundary case and
the associated Gibbs measure n,β on the n th generation, which is also the polymer …

We consider directed polymers in random environment on the lattice Z d at small inverse
temperature and dimension d≥ 3. Then, the normalized partition function W n is a regular …

We study a directed polymer model defined on a hierarchical diamond lattice, where the
lattice is constructed recursively through a recipe depending on a branching number b∈ N …

Disordered systems such as spin glasses have been used extensively as models for high-
dimensional random landscapes and studied from the perspective of optimization …

Le mouvement brownien branchant (BBM) est un système de particules se déplaçant et se
reproduisant aléatoirement. En premier lieu, nous étudions avec précision la transition de …

We consider a model for a directed polymer in a random environment defined on a
hierarchical diamond lattice in which iid random variables are attached to the lattice bonds …

This thesis explores the algorithmic perspectives of the branching random walk and the
continuous random energy model (CREM). Namely, we are interested in constructing …