Anomalous dynamical scaling determines universal critical singularities

Abstract

Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived and shown to imply universal singularities in the normalized cumulant generator. Exact calculations for continuous time random walks provide paradigmatic examples connected with singularities of second order phase transitions. In the biased case scaling is restricted to displacements in the drift direction and singularities have no equilibrium analogue.

References in corpus (32)

• The large deviation approach to statistical mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fractional calculus and continuous-time finance
• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
• On the strong anomalous diffusion
• A continuous time random walk model for financial distributions
• Relative dispersion in fully developed turbulence: The Richardson's Law and Intermittency Corrections
• The Continuous Time Random Walk, still trendy: Fifty-year history, state of art, and outlook
• Probability distribution of the order parameter for the 3D Ising model universality class: a high precision Monte Carlo study
• Exact Coarse Graining Preserves Entropy Production out of Equilibrium
• Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent?
• Anomalous scaling of dynamical large deviations
• Fluctuation relations for anomalous dynamics
• Universal fluctuations in subdiffusive transport
• Large deviations for continuous time random walks
• Eigenvalue crossing as a phase transition in relaxation dynamics
• Melting and unzipping of DNA
• Rare events and scaling properties in field-induced anomalous dynamics
• Anomalous scaling and first-order dynamical phase transition in large deviations of the Ornstein-Uhlenbeck process
• Correlated continuous-time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics
• Large Deviation in Continuous Time Random Walks
• Universal singularities of anomalous diffusion in the Richardson class
• Fluctuation relations without uniform large deviations
• Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations
• Noise correction of large deviations with anomalous scaling
• Probability distribution functions of sub- and super-diffusive systems
• Overlap Distribution of the Three-Dimensional Ising Model
• Rate dependence of current and fluctuations in jump models with negative differential mobility
• Multicanonical Simulations of the Tails of the Order-Parameter Distribution of the Two-Dimensional Ising Model

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• Relaxation shortcuts through boundary coupling
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• Universal singularities of anomalous diffusion in the Richardson class
• Time-fractional Caputo derivative versus other integro-differential operators in generalized Fokker-Planck and generalized Langevin equations
• A sluggish random walk with subdiffusive spread
• Generalized arcsine laws for a sluggish random walker with subdiffusive growth
• Generalization of the Central Limit Theorem to Critical Systems: Revisiting Perturbation Theory
• Partial versus total resetting for Lévy flights in d dimensions: similarities and discrepancies
• Universal and non-universal large deviations in critical systems
• Critical Probability Distributions of the order parameter at two loops I: Ising universality class
• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Understanding random-walk dynamical phase coexistence through waiting times
• Universal and non-universal signatures in the scaling functions of critical variables
• Critical Probability Distributions of the order parameter at two loops II: $O(n)$ universality class
• Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting