Carlo did his Bachelor’s in Statistics (with some economics) in Milano then moved to Torino for a Master’s in Stochastics and Data Science. He enjoys both statistics and probability and his Master’s project was on an application of Bayesian Nonparametric to DNA sequencing. He likes (watching) sports, mainly regular football, American football and cycling, going to the sea in the summer (who doesn’t) and eating carbonara.

Research project title:
Scaling Limits for Random Walks on Random Conductances

Supervisor(s):
Daniel Kious, Alexandre Stauffer

Project description:
Random walks on random conductances form a well-established class of motions in random environment, that has already been investigated in depth. In the case where the conductances are bounded away from zero and infinity, it is well-known that the re-scaled walk converges to a Brownian motion. Out of this regime, this model showcases “trapping phenomena”, that is, a slow down in the walk due to the presence of small areas in the environment that behave atypically. In this case, the usual invariance principle does not hold anymore. Although this mechanism is now well identified, it is challenging to obtain, in the trapped regimes, functional scaling limits and other fine results (e.g. aging, quenched convergence). Carlo’s project explores trapping phenomena for random walks in random environments and on random graphs. In particular, Carlo will investigate the relationship between the Bouchaud Trap Model and random walks on random conductances in the trapped regimes.