In the course of my habilitation, I researched random walks and some of their applications to statistical physics and random access algorithms. In this talk, I will first give a brief overview of the different papers which constitute the habilitation. I will then talk about the recent work "Off-diagonal long-range order for the free bosonic loop soup" in greater detail. In this work, we give a new (probabilistic) proof for condensation of the free Bose gas, irrespective of boundary condition. The result is based on the Feynman-Kac formula, combined with large deviation estimates and previous results on random partitions. Joint work with Wolfgang König and Alexander Zass.