Open Access
2015 The glassy phase of the complex branching Brownian motion energy model
Lisa Hartung, Anton Klimovsky
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Electron. Commun. Probab. 20: 1-15 (2015). DOI: 10.1214/ECP.v20-4360


We identify the fluctuations of the partition function for a class of random energy models, where the energies are given by the positions of the particles of the complex-valued branching Brownian motion (BBM). Specifically, we provide the weak limit theorems for the partition function in the so-called "glassy phase'' – the regime of parameters, where the behaviour of the partition function is governed by the extrema of BBM. We allow for arbitrary correlations between the real and imaginary parts of the energies. This extends the recent result of Madaule, Rhodes and Vargas (2013), where the uncorrelated case was treated. Inparticular, our result covers the case of the real-valued BBM energy model at complex temperatures.


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Lisa Hartung. Anton Klimovsky. "The glassy phase of the complex branching Brownian motion energy model." Electron. Commun. Probab. 20 1 - 15, 2015.


Accepted: 27 October 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60303
MathSciNet: MR3417450
Digital Object Identifier: 10.1214/ECP.v20-4360

Primary: 60J80
Secondary: 60F05 , 60G70 , 60K35 , 82B44

Keywords: Branching Brownian motion , cluster processes , extremal processes , Gaussian processes , logarithmic correlations , multiplicative chaos , phase diagram , random energy model

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