English

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 L1L^1 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