Complex Random Energy Model: Zeros and Fluctuations

Details Complex Random Energy Model: Zeros and Fluctuations Complex Random Energy Model: Zeros and Fluctuations

2012-01-24

arxiv.org/abs/1201.5098v2

Mathematics

Probability

22 pages

Scientific paper

The partition function of the random energy model at inverse temperature $\beta$ is defined by $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables, and $n=\log N$. We identify the asymptotic structure of complex zeros of $Z_N$, as $N\to\infty$, confirming predictions made in the theoretical physics literature. Also, we describe the limiting complex fluctuations for a model generalizing $Z_N(\beta)$.

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