Exact asymptotics of the freezing transition of a logarithmically correlated random energy model

Abstract

We consider a logarithmically correlated random energy model, namely a model for directed polymers on a Cayley tree, which was introduced by Derrida and Spohn. We prove asymptotic properties of a generating function of the partition function of the model by studying a discrete time analogy of the KPP-equation - thus translating Bramson's work on the KPP-equation into a discrete time case. We also discuss connections to extreme value statistics of a branching random walk and a rescaled multiplicative cascade measure beyond the critical point.

References in corpus (5)

• Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential
• Minima in branching random walks
• KPZ in one dimensional random geometry of multiplicative cascades
• Tightness for a family of recursion equations
• Duality and KPZ in Liouville Quantum Gravity

Cited by in corpus (15)

• Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function
• Freezing and decorated Poisson point processes
• Gaussian multiplicative chaos and KPZ duality
• Critical Mandelbrot Cascades
• On the partition function of the Riemann zeta function, and the Fyodorov--Hiary--Keating conjecture
• Gaussian multiplicative chaos and applications: a review
• The Fyodorov-Hiary-Keating Conjecture. I
• Hausdorff and packing spectra, large deviations, and free energy for branching random walks in ${\mathbb{R}}^d$
• Basic properties of critical lognormal multiplicative chaos
• Branching Brownian motion with selection
• The uniqueness of the Gaussian multiplicative chaos revisited
• The subleading order of two dimensional cover times
• Towards rigorous analysis of the Levitov-Mirlin-Evers recursion
• Glassy phase and freezing of log-correlated Gaussian potentials
• On exact scaling log-Infinitely divisible cascades