The branching-ruin number of a tree, which describes its asymptotic growth and geometry,
can be seen as a polynomial version of the branching number. This quantity was defined by …

arXiv:2210.07825v2 [math.PR] 4 Sep 2023 Page 1 Quenched invariance principle for biased
random walks in random conductances in the sub-ballistic regime Alexander Fribergh ∗ Tanguy …

We study biased random walk on the infinite connected component of supercritical
percolation on the integer lattice Z d for d≥ 2. For this model, Fribergh and Hammond …

We consider random walks amongst random conductances in the cases where the
conductances can be arbitrarily small, with a heavy-tailed distribution at 0, and where the …

We consider a one-dimensional random walk among biased iid conductances, in the case
where the random walk is transient but sub-ballistic: this occurs when the conductances …

We consider two models of one-dimensional random walks among biased iid random
conductances: the first is the classical exponential tilt of the conductances, while the second …

We consider biased random walks in a one-dimensional percolation model. This model
goes back to Axelson-Fisk and Häggström and exhibits the same phase transition as biased …

Nous présentons d'abord une introduction au sujet des marches aléatoires en milieux
aléatoires. Nous nous penchons en particulier sur les phénomènes de ralentissement, et …

We look at random walks in Dirichlet environment. It was known that in dimension $ d\geq
3$, if the walk is sub-ballistic, the displacement of the walk is polynomial of order $\kappa …

This thesis is at the interface between combinatorics and probability, and contributes to the
study of a few models stemming from statisticalmechanics: polymers, self-interacting random …