Talks' abstracts > Portillo Del Valle Daniela

We provide strong convergence results for random walks with echoed steps, that is, a step-reinforced walk with randomness induced into the magnitude of reinforcement of the increments. This is a broad generalization of the positively/negatively/unbalanced step-reinforced random walks and the elephant random walk, which arise from insertion of memory in the dynamics of an ordinary random walk. Continuous time branching random walks, Pólya urns and random recursive trees are strongly connected to this model, and thus are the means to derive laws of large numbers and characterize the conditions of convergence towards non-trivial limits, which can often be expressed as random series.