UC Santa Barbara
Mean-field replica theory: review of basics and a new approach
Wednesday 31st of October 2012 at 12:00pm
Replica theory provides a general method for evaluating the mode of a distribution, and has varied applications to problems in statistical mechanics, signal processing, etc. Evaluation of the formal expressions arising in replica theory represents a formidable technical challenge, but one that physicists have apparently intuited correct methods for handling. In this talk, I will first provide a review of the historical development of replica theory, covering: 1) motivation, 2) the intuited ``Parisi-ansatz" solution, 3) continued controversies, and 4) a survey of applications (including to neural networks). Following this, I will discuss an exploratory effort of mine, aimed at developing an ansatz-free solution method. As an example, I will work out the phase diagram for a simple spin-glass model. This talk is intended primarily as a tutorial.
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