The Continuous Time Random Walk, still trendy: Fifty-year history, state of art, and outlook

Abstract

In this issue we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism and its numerous modifications thanks to their flexibility and various applications as well its promising perspectives in different fields of knowledge. A short review of significant achievements and possibilities is given, however, still far from completeness.

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• Lévy walks
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals
• Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
• Use and Abuse of a Fractional Fokker-Planck Dynamics for Time-Dependent Driving
• Weakly non-ergodic Statistical Physics
• Photon Counting Statistics For Blinking CdSe-ZnS Quantum Dots: A Levy Walk Process
• The continuous time random walk formalism in financial markets
• Infinite densities for Lévy walks
• Fractional Fokker-Planck equation for Lévy flights in nonhomogeneous environments
• A model for interevent times with long tails and multifractality in human communications: An application to financial trading
• Space-time velocity correlation function for random walks
• Non-independent continuous time random walks
• Power-law velocity distributions in granular gases
• Fractional Fokker-Planck subdiffusion in alternating fields
• Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction

Cited by in corpus (38)

• Random walks and diffusion on networks
• The role of fractional time-derivative operators on anomalous diffusion
• Fractional advection-diffusion-asymmetry equation
• Continuous-time random-walk model for anomalous diffusion in expanding media
• Large deviations for continuous time random walks
• Transport in disordered systems: the single big jump approach
• Renewal theory with fat tailed distributed sojourn times: typical versus rare
• Anomalous dispersion in correlated porous media: A coupled continuous time random walk approach
• Quenched and Annealed Disorder Mechanisms in Comb-Models with Fractional Operators
• Scale invariant Green-Kubo relation for time averaged diffusivity
• Should I stay or should I go? Zero-size jumps in random walks for Lévy flights
• Transitions in the ergodicity of subrecoil-laser-cooled gases
• Operationally Accessible Uncertainty Relations for Thermodynamically Consistent Semi-Markov Processes
• Anomalous dynamical scaling determines universal critical singularities
• Local time for run and tumble particle
• Continuous time random walks and Fokker-Planck equation in expanding media
• Anomalous diffusion originated by two Markovian hopping-trap mechanisms
• Generalized fractional Poisson process and related stochastic dynamics
• Continuous time random walk and diffusion with generalized fractional Poisson process
• On Discrete Time Prabhakar-Generalized Fractional Poisson Processes and Related Stochastic Dynamics
• Extreme value theory for constrained physical systems
• Biased continuous-time random walks with Mittag-Leffler jumps
• Random walk on temporal networks with lasting edges
• Active Random Walks in One and Two Dimensions
• Towards a Universal Measure of Complexity
• First passage statistics of active random walks on one and two dimensional lattices
• Gas of sub-recoiled laser cooled atoms described by infinite ergodic theory
• Random walks on networks with preferential cumulative damage: Generation of bias and aging
• Limit theorems for cloning algorithms
• Understanding the nature of the long-range memory phenomenon in socioeconomic systems
• Approximation of the first passage time distribution for the birth-death processes
• Rare Events and Single Big Jump Effects in Ornstein-Uhlenbeck Processes
• The Transient Case of The Quenched Trap Model
• Siegmund duality for physicists: a bridge between spatial and first-passage properties of continuous and discrete time stochastic processes
• Simulation of the continuous-time random walk using subordination schemes
• Two-dimensional Brownian motion with dependent components: turning angle analysis
• Directed Continuous-Time Random Walk with memory
• Asymmetric random walks with bias generated by discrete-time counting processes