The phase diagram of the complex branching Brownian motion energy model
Probability
2017-04-19 v1 Disordered Systems and Neural Networks
Abstract
We complete the analysis of the phase diagram of the complex branching Brownian motion energy model by studying Phases I, III and boundaries between all three phases (I-III) of this model. For the properly rescaled partition function, in Phase III and on the boundaries I/III and II/III, we prove a central limit theorem with a random variance. In Phase I and on the boundary I/II, we prove an a.s. and martingale convergence. All results are shown for any given correlation between the real and imaginary parts of the random energy.
Keywords
Cite
@article{arxiv.1704.05402,
title = {The phase diagram of the complex branching Brownian motion energy model},
author = {Lisa Hartung and Anton Klimovsky},
journal= {arXiv preprint arXiv:1704.05402},
year = {2017}
}
Comments
22 pages, 2 figures