Complex random energy model : zeros and fluctuations

Z. Kabluchko, A. Klimovsky

Research output: Book/ReportReportAcademic

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Abstract

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 languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages22
Publication statusPublished - 2012

Publication series

NameReport Eurandom
Volume2012002
ISSN (Print)1389-2355

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