Mean first-passage times of non-Markovian random walkers in confinement

Abstract

The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the efficiency of processes as varied as diffusion-limited reactions, target search processes or spreading of diseases. Most methods to determine the FPT properties in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects can not be neglected. Examples of non Markovian dynamics include single-file diffusion in narrow channels or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics \cite{turiv2013effect}, dense soft colloids or viscoelastic solution. Here, we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean FPT of a Gaussian non-Markovian random walker to a target point. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the trajectory of the random walker in the future of the first-passage event, which are shown to govern the FPT kinetics.This analysis is applicable to a broad range of stochastic processes, possibly correlated at long-times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes including the emblematic case of the Fractional Brownian Motion in one or higher dimensions. These results show, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.

Submitted version. Supplementary Information can be found on the Nature website : http://www.nature.com/nature/journal/v534/n7607/full/nature18272.html

References in corpus (3)

• First-passage times in complex scale-invariant media
• Non-Markovian polymer reaction kinetics
• Anomalous Polymer Dynamics Is Non-Markovian: Memory Effects and The Generalized Langevin Equation Formulation

Cited by in corpus (36)

• Generalized arcsine laws for fractional Brownian motion
• Inverse square Lévy walks are not optimal search strategies for $d\ge 2$
• Emergence of molecular friction in liquids: bridging between the atomistic and hydrodynamic pictures
• Learning physical properties of anomalous random walks using graph neural networks
• Optimal non-Markovian search strategies with n-step memory
• Survival probability of stochastic processes beyond persistence exponents
• First-encounter time of two diffusing particles in confinement
• Everlasting impact of initial perturbations on first-passage times of non-Markovian random walks
• Reliability modeling and statistical analysis of accelerated degradation process with memory effects and unit-to-unit variability
• An encounter-based approach to the escape problem
• Long-term memory induced correction to Arrhenius law
• Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime
• Exact enumeration approach to first-passage time distribution of non-Markov random walks
• First-encounter time of two diffusing particles in two- and three-dimensional confinement
• Persistent and anti-Persistent Motion in Bounded and Unbounded Space: Resolution of the First-Passage Problem
• Search efficiency of biased migration towards stationary or moving targets in heterogeneously structured environments
• Target finding in fibrous biological environments
• Evidence and quantification of memory effects in competitive first passage events
• Non-stationary Markovian Replication Process causing Diverse Diffusions
• Survival in a nanoforest of absorbing pillars
• Unexpected advantages of exploitation for target searches in complex networks
• Memory in random bouncing ball dynamics
• Universal Negative Energetic Elasticity in Polymer Chains: Crossovers among Random, Self-Avoiding, and Neighbor-Avoiding Walks
• Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems
• Mean first-passage time of an anisotropic diffusive searcher
• Sign-changes as a universal concept in first-passage time calculations
• Interface Collisions
• Brownian motion: from kinetics to hydrodynamics
• Concentration of Empirical First-Passage Times
• Fractionally Quantized Recurrence Detection Times in Monitored Quantum Many-Body Systems
• Functionals of fractional Brownian motion and the three arcsine laws
• Trapping problem on star-type graphs with applications
• Optimization of multisite reactions in complex compartmentalized media
• Anomalous Diffusion and Emergent Universality in Coupled Memory-Driven Systems
• Universal Linear Response of First-Passage Kinetics: A Framework for Prediction and Inference
• Encounter-based approach to target search problems: a review