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 $X_1, X_2, \ldots$
are independent real standard normal random variables, and $n = log N$. We identify the asymptotic structure of complex zeros of $Z_N$, as $N \rightarrow \infty$, confirming predictions made in the theoretical physics literature. Also, we describe the limiting complex fluctuations for a model generalizing $Z_N(\beta)$.

Original language | English |
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Place of Publication | Eindhoven |
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Publisher | Eurandom |
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Number of pages | 22 |
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Publication status | Published - 2012 |
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Name | Report Eurandom |
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Volume | 2012002 |
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ISSN (Print) | 1389-2355 |
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