CAREER: New Information Processing Techniques from Statistical Physics and Probability Theory

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Statistical mechanics aims at understanding the collective behavior of large systems made of simple interacting components. The space of possible configurations of such systems is high-dimensional and combinatorial and, as a consequence, it is extremely challenging to understand their behavior. Despite this, statistical mechanics techniques often provide strong quantitative predictions.A number of modern information technologies share the same complex features, in that they are based on large decentralized networks of simple units. Examples include sensor networks, ad hoc wireless networks, social communities, modern coding systems. Over the last 20 years, spectacular progress has been made in probability theory towards a rigorization of the methods of statistical mechanics. These achievements can have far-reaching consequences in the analysis and design of computer and communication systems.The present proposal has two goals: (I) Clarify and rigorize the statistical physics techniques and their applications to engineering and computer science. (II) Use this approach in three new application domains: learning graphical models; detection and measurement through sparse graphs; statistical inference for high-dimensional combinatorial distributions.