Continuous Gated First-Passage Processes
arXiv:2211.09164 · doi:10.1088/1361-6633/ad7530
Abstract
Gated first-passage processes, where completion depends on both hitting a target and satisfying additional constraints, are prevalent across various fields. Despite their significance, analytical solutions to basic problems remain unknown, e.g. the detection time of a diffusing particle by a gated interval, disk, or sphere. In this paper, we elucidate the challenges posed by continuous gated first-passage processes and present a renewal framework to overcome them. This framework offers a unified approach for a wide range of problems, including those with single-point, half-line, and interval targets. The latter have so far evaded exact solutions. Our analysis reveals that solutions to gated problems can be obtained directly from the ungated dynamics. This, in turn, reveals universal properties and asymptotic behaviors, shedding light on cryptic intermediate-time regimes and refining the notion of high-crypticity for continuous-space gated processes. Moreover, we extend our formalism to higher dimensions, showcasing its versatility and applicability. Overall, this work provides valuable insights into the dynamics of continuous gated first-passage processes and offers analytical tools for studying them across diverse domains.
arXiv comment26 pages, 6 figures
References in corpus (52)
- Diffusion with Stochastic Resetting
- Stochastic Resetting and Applications
- First Passage Under Restart
- Optimal stochastic restart renders fluctuations in first passage times universal
- Run and tumble particle under resetting: a renewal approach
- Extreme value statistics of correlated random variables: a pedagogical review
- First passage under stochastic resetting in an interval
- Records in stochastic processes -- Theory and applications
- On the Role of Global Warming on the Statistics of Record-Breaking Temperatures
- Universal Record Statistics of Random Walks and Lévy Flights
- Search with home returns provides advantage under high uncertainty
- Large deviations for Markov processes with resetting
- Paradigm shift in diffusion-mediated surface phenomena
- The inspection paradox in stochastic resetting
- Scaled Brownian motion with renewal resetting
- Work fluctuations and Jarzynski equality in stochastic resetting
- Péclet number governs transition to acceleratory restart in drift-diffusion
- Hitting Time Distributions in Financial Markets
- Random Walks in Logarithmic and Power-Law Potentials, Nonuniversal Persistence, and Vortex Dynamics in the Two-Dimensional XY Model
- Diffusion with resetting in a logarithmic potential
- Optimization in First-Passage Resetting
- Extreme events on complex networks
- First passage under restart with branching
- Kinetics of stochastically-gated diffusion-limited reactions and geometry of random walk trajectories
- Record statistics for biased random walks, with an application to financial data
- First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
- Record statistics of a strongly correlated time series: random walks and Lévy flights
- First passage time statistics for two-channel diffusion
- First-passage and first-exit times of a Bessel-like stochastic process
- Space-dependent diffusion with stochastic resetting: A first-passage study
- ``Weather'' Records: Musings on Cold Days after a Long Hot Indian Summer
- Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
- Surface Hopping Propagator: An Alternative Approach to Diffusion-Influenced Reactions
- Mean-performance of sharp restart I: Statistical roadmap
- Diffusive search for a stochastically-gated target with resetting
- Universal framework for record ages under restart
- First hitting times to intermittent targets
- Record statistics of financial time series and geometric random walks
- A Unified Approach to Gated Reactions on Networks
- Molecular search with conformational change: One-dimensional discrete-state stochastic model
- Rate enhancement of gated drift-diffusion process by optimal resetting
- Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties
- Extreme events in stochastic transport on networks
- First-passage times of multiple diffusing particles with reversible target-binding kinetics
- First hitting times between a run-and-tumble particle and a stochastically-gated target
- Reversible Target-Binding Kinetics of Multiple Impatient Particles
- Escape of a Sticky Particle
- Inference from gated first-passage times
- First detection of threshold crossing events under intermittent sensing
- Generalized model of blockage in particulate flow limited by channel carrying capacity
- Stochastic models of multi-channel particulate transport with blockage
- Gated reactions in discrete time and space