The phase diagram of the complex branching Brownian motion energy model

DOI10.1214/18-EJP245zbMath1406.60119arXiv1704.05402OpenAlexW2963320578MaRDI QIDQ1722024

Lisa Hartung, Anton Klimovsky

Publication date: 14 February 2019

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.05402

zbMATH Keywords

Gaussian processescentral limit theoremphase diagramrandom energy modelmartingale convergencebranching Brownian motionrandom variancelogarithmic correlations

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Extreme value theory; extremal stochastic processes (60G70) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (7)

Convergence in law for complex Gaussian multiplicative chaos in phase III ⋮ Secular coefficients and the holomorphic multiplicative chaos ⋮ Stable-like fluctuations of Biggins' martingales ⋮ Fluctuations of Biggins' martingales at complex parameters ⋮ 1-stable fluctuations in branching Brownian motion at critical temperature. I: The derivative martingale ⋮ On \(L^p\)-convergence of the Biggins martingale with complex parameter ⋮ A universality result for subcritical complex Gaussian multiplicative chaos

Cites Work

• Unnamed Item
• Gaussian multiplicative chaos and applications: a review
• Maximum of the characteristic polynomial of random unitary matrices
• Convergence of complex martingales in the branching random walk: the boundary
• Maxima of a randomized Riemann zeta function, and branching random walks
• The glassy phase of the complex branching Brownian motion energy model
• Uniform convergence for complex [0,1-martingales]
• Convergence of complex multiplicative cascades
• A conditional limit theorem for the frontier of a branching Brownian motion
• Mean field theory of directed polymers with random complex weights
• Derrida's generalised random energy models. I: Models with finitely many hierarchies
• Derrida's generalized random energy models. II: Models with continuous hierarchies
• Fixed points of the smoothing transform: two-sided solutions
• Fluctuations of Biggins' martingales at complex parameters
• The Riemann zeta function and Gaussian multiplicative chaos: statistics on the critical line
• The glassy phase of complex branching Brownian motion
• 1-stable fluctuations in branching Brownian motion at critical temperature. I: The derivative martingale
• Complex Gaussian multiplicative chaos
• Solutions to complex smoothing equations
• Complex random energy model: zeros and fluctuations
• The Seneta-Heyde scaling for the branching random walk
• The dynamical sine-Gordon model
• The extremal process of two-speed branching Brownian motion
• Imaginary multiplicative chaos: moments, regularity and connections to the Ising model
• Derrida’s Random Energy Models
• Gaussian Processes on Trees
• A central limit theorem and a law of the iterated logarithm for the Biggins martingale of the supercritical branching random walk
• The Sherrington-Kirkpatrick Model
• Fixed points of multivariate smoothing transforms with scalar weights
• Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model

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