# One step replica symmetry breaking and extreme order statistics of logarithmic REMs

@article{Cao2016OneSR, title={One step replica symmetry breaking and extreme order statistics of logarithmic REMs}, author={Xiangyu Cao and Yan V. Fyodorov and Pierre Le Doussal}, journal={arXiv: Statistical Mechanics}, year={2016} }

Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models (logREMs) behave in the thermodynamic limit as a randomly shifted decorated exponential Poisson point process. The distribution of the random shift is determined solely by the large-distance ("infra-red", IR) limit of the model, and is equal to the free energy…

## 11 Citations

Disordered statistical physics in low dimensions: extremes, glass transition, and localization

- Computer Science
- 2017

This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transitions in long-range random matrices, and argues that such localization transitions occur generically in the broadly distributed class.

Finite Size Corrections to the Parisi Overlap Function in the GREM

- Mathematics
- 2017

We investigate the effects of finite size corrections on the overlap probabilities in the Generalized Random Energy Model in two situations where replica symmetry is broken in the thermodynamic…

Log-correlated random-energy models with extensive free-energy fluctuations: Pathologies caused by rare events as signatures of phase transitions.

- PhysicsPhysical review. E
- 2018

It is argued that a seemingly nonphysical vanishing of the moment generating function for some values of parameters is related to the termination point transition (i.e., prefreezing), and the associated universal log corrections in the frozen phase are studied, both for logREMs and for the standard REM.

Extremes of log-correlated random fields and the Riemann zeta function, and some asymptotic results for various estimators in statistics

- Mathematics
- 2019

In this paper, we study a random field constructed from the two-dimensional Gaussian free field (GFF) by modifying the variance along the scales in the neighborhood of each point. The construction…

A review of conjectured laws of total mass of Bacry–Muzy GMC measures on the interval and circle and their applications

- MathematicsReviews in Mathematical Physics
- 2018

Selberg and Morris integral probability distributions are long conjectured to be distributions of the total mass of the Bacry–Muzy Gaussian Multiplicative Chaos measures with non-random logarithmic…

Statistics of Extremes in Eigenvalue-Counting Staircases.

- MathematicsPhysical review letters
- 2020

An extended Fisher-Hartwig conjecture supplemented with the freezing duality conjecture for log-correlated fields is used to obtain the cumulants of the distribution of that maximum for any β>0, and the results are expected to apply to the statistics of zeroes of the Riemann Zeta function.

A Theory of Intermittency Differentiation of 1D Infinitely Divisible Multiplicative Chaos Measures

- Mathematics
- 2018

A theory of intermittency differentiation is developed for a general class of 1D infinitely divisible multiplicative chaos measures. The intermittency invariance of the underlying infinitely…

Physique statistique des systèmes désordonnées en basses dimensions

- Physics
- 2017

Cette these presente des resultats nouveaux dans deux sujets de la physique statistique du desordre: les modeles aux energies aleatoires logarithmiquement correlees (logREMs), et la transition de…

Geometry of the Gibbs measure for the discrete 2D
Gaussian free field with scale-dependent variance

- MathematicsLatin American Journal of Probability and Mathematical Statistics
- 2017

We continue our study of the scale-inhomogeneous Gaussian free field introduced in Arguin and Ouimet (2016). Firstly, we compute the limiting free energy on V_N and adapt a technique of Bovier and…

A family of probability distributions consistent with the DOZZ formula: towards a conjecture for the law of 2D GMC

- MathematicsProbability and Mathematical Physics
- 2021

A three parameter family of probability distributions is constructed such that its Mellin transform is defined over the same domain as the 2D GMC on the Riemann sphere with three insertion points…

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