Complex random energy model: zeros and fluctuations

• 成果类型: Article
• 署名作者: Kabluchko, Zakhar; Klimovsky, Anton
• 署名单位: Ulm University; Leiden University; Leiden University - Excl LUMC
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0480-5
• 发表日期: 2014
• 页码: 159-196
• 关键词: statistical-mechanics; partition-function; LIMIT-THEOREMS; sums; LAWS; rem

摘要

The partition function of the random energy model at inverse temperature is a sum of random exponentials , where are independent real standard normal random variables (=random energies), and . We study the large N limit of the partition function viewed as an analytic function of the complex variable . We identify the asymptotic structure of complex zeros of the partition function confirming and extending predictions made in the theoretical physics literature. We prove limit theorems for the random partition function at complex , both on the logarithmic scale and on the level of limiting distributions. Our results cover also the case of the sums of independent identically distributed random exponentials with any given correlations between the real and imaginary parts of the random exponent.