Complex random energy model: zeros and fluctuations

DOI10.1007/s00440-013-0480-5zbMath1292.60052arXiv1201.5098OpenAlexW3105470215MaRDI QIDQ2447284

Zakhar Kabluchko, Anton Klimovsky

Publication date: 25 April 2014

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.5098

zbMATH Keywords

central limit theoremstable distributionsextreme value theorylogarithmic potentialsrandom energy modelzeros of random analytic functionssums of random exponentials

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44)

Related Items (9)

Convergence in law for complex Gaussian multiplicative chaos in phase III ⋮ Limit theorems for the alloy-type random energy model ⋮ Limit theorems for random Dirichlet series ⋮ The phase diagram of the complex branching Brownian motion energy model ⋮ The glassy phase of complex branching Brownian motion ⋮ 1-stable fluctuations in branching Brownian motion at critical temperature. I: The derivative martingale ⋮ Critical points of random polynomials with independent identically distributed roots ⋮ Complex Gaussian multiplicative chaos ⋮ A universality result for subcritical complex Gaussian multiplicative chaos

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic distribution of complex zeros of random analytic functions
• On a third-order phase transition
• Functional limit theorems for sums of independent geometric Lévy processes
• Limit laws for sums of products of exponentials of iid random variables
• Limit laws for power sums and norms of i.i.d. samples
• Limit laws for norms of IID samples with Weibull tails
• The first zero of an empirical characteristic function
• On the existence of thermodynamics for the random energy model
• Limit behaviour of the empirical characteristic function
• Uniform convergence of martingales in the branching random walk
• The empirical characteristic function and its applications
• Mean field theory of directed polymers with random complex weights
• Fluctuations of the free energy in the REM and the \(p\)-spin SK models
• Asymptotic equivalence of probability distributions with applications to some problems of asymptotic independence
• Limit theorems for sums of random exponentials
• On the convergence of sums of independent Banach space valued random variables
• Replica analysis of partition-function zeros in spin-glass models
• Random-energy model: An exactly solvable model of disordered systems
• Analyticity of the partition function of the random energy model
• Partition-function zeros of spherical spin glasses and their relevance to chaos
• Statistical Mechanics of Disordered Systems
• Critical points of random polynomials with independent identically distributed roots
• STATISTICAL MECHANICS OF EQUILIBRIUM AND NONEQUILIBRIUM PHASE TRANSITIONS: THE YANG–LEE FORMALISM
• Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation
• Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
• Mean Field Models for Spin Glasses

This page was built for publication: Complex random energy model: zeros and fluctuations