Central approximation in statistical physics and information theory

In statistical physics and information theory, while asymptotic behavior of the partition function is often of our primary interest, the most of works are dedicated to analysis of the exponent of the partition function. In our previous paper on sparse random factor graph ensembles, we show that the exponent of the expectation of the partition function is represented as the minimum of the Bethe free energy of the small averaged graph by using the method of types. In this paper, we present a general framework to study more precise asymptotic behaviors of the partition function, using the central approximation in conjunction with the method of types.