Real-Space Renormalization for disordered systems at the level of Large Deviations

Abstract

The real-space renormalization procedures on hierarchical lattices have been much studied for many disordered systems in the past at the level of their typical fluctuations. In the present paper, the goal is to analyze instead the renormalization flows for the tails of probability distributions in order to extract the scalings of their large deviations and the tails behaviors of the corresponding rate functions. We focus on the renormalization rule for the ground-state energy of the Directed Polymer model in a random medium, and study the various renormalization flows that can emerge for the tails as a function of the tails of the initial condition.

v2=revised version, 17 pages, 1 figure

References in corpus (14)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation theorems for stochastic dynamics
• Large Deviations of Extreme Eigenvalues of Random Matrices
• Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
• Finite-size scaling in extreme statistics
• Condensation and Extreme Value Statistics
• Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics
• Condensation transition in joint large deviations of linear statistics
• Revisiting classical and quantum disordered systems from the unifying perspective of large deviations
• Renormalization flow in extreme value statistics
• Critical points of quadratic renormalizations of random variables and phase transitions of disordered polymer models on diamond lattices
• Condensation for random variables conditioned by the value of their sum
• Critical behavior of interfaces in disordered Potts ferromagnets : statistics of free-energy, energy and interfacial adsorption

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