Trust management, broadly intended as the ability to maintain belief relationship among entities, is recognized as a fundamental security challenge for autonomous and selforganizing networks. In this work, we focus on the evaluation process of trust evidence in distributed networks, where no pre-established infrastructure can be assumed. After casting the problem into the framework of Estimation Theory, a distributed Maximum Likelihood trust estimation algorithm is proposed. Strong parallels with Spin Glasses Theory are shown, providing key insights about the algorithm performance and limitations, as well as useful formulas for parameters tuning. This work presents a mathematically rigorous analytical approach to the problem, and proposes the use of statistical physics methods not only to understand the complex dynamics that arise from the interactions of peers in decentralized networks but also to design robust protocols and algorithms whose performance can be rigorously evaluated.