Abstract: We are interested in the recurrence and transience of a branching random walk in Z^d indexed by a critical Galton-Watson tree conditioned to survive. When the environment is homogeneous, deterministic, and if the offspring distribution has a second moment, it is known to be recurrent for d at most 4, and transient for d larger than 4. In this talk we consider an environment made of random conductances, and we prove that, if the conductances satisfy suitable technical assumptions, the same result holds. The argument is based on the combination of a 0-1 law and a truncated second moment method, which only requires to have good estimates on the quenched Green's function of a (non-branching) random walk in random conductances. This is a joint work with Christophe Sabot and Bruno Schapira.
The critical random walk snake in random conductances
28.11.2024 13:15 - 15:00
Organiser:
W. da Silva, M. Lis
Location: