1201.5098 (Zakhar Kabluchko et al.)

Complex Random Energy Model: Zeros and Fluctuations    [PDF]

Zakhar Kabluchko, Anton Klimovsky

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 $Z_N(\beta)$.

View original: http://arxiv.org/abs/1201.5098