Joint ICME/Probability Seminar. Presentation by Andrea Montanari, Asst. Prof. in EE and Statistics. Abstact- Phase transitions, i.e. abrupt changes in the macroscopic properties of a system as some control parameter is varied, are a main object of study for statistical physics. It has recently become clear that their occurrence is of interest to other domains, ranging from applied probability to random combinatorics and coding. In this talk I will discuss a major phenomenon related to phase transitions: the emergence of scaling properties in the vicinity of the transition point. I will present an example in which such a scaling behavior can be computed exactly and explain its relation to random satisfiability problems and iterative coding systems. Most interestingly, this result can be used to optimize low density parity check codes for communication over the erasure channel at finite blocklength. [Based on joint work with A.Amraoui, T.Richardson, R.Urbanke and A.Dembo]