Purpose of this thesis is to describe the recently developed theory of Schrdinger bridges for Markov chains, and to investigate its effectiveness by simulation on various examples. Particular interest to us are chains that converges slowly to the equilibrium distribution such as those that arise from random geometric graphs. Bridges allow in principle the possibility of controlling a chain to its invariant distribution in finite time. Manca giusto il Papa. Non sono insinuazioni, sono dati di fatto. E dovere di…