Capture of the lamb: Diffusing predators seeking a diffusing prey

We study the capture of a diffusing “lamb” by diffusing “lions” in one dimension. The capture dynamics is exactly soluble by probabilistic techniques when the number of lions is very small, and is tractable by extreme statistics considerations when the number of lions is very large. However, the exact solution for the general case of three or more lions is still not known.

• Publication year

  1999

• Venue

  American Journal of Physics

• Publication date

  1999-05-20

• Fields of study

  Biology, Physics

• Identifiers
  DOI 10.1119/1.19115arXiv cond-mat/9905299
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• “Weather” records: Musings on cold days after a long hot Indian summer

  1999cited by this paper
• Kinetics of a diffusive capture process: lamb besieged by a pride of lions

  1996cited by this paper
• Scaling: Self-similarity and intermediate asymptotics

  1996cited by this paper
• Life and death in an expanding cage and at the edge of a receding cliff

  1995cited by this paper
• Aspects and applications of the random walk

  1995cited by this paper
• Aspects and Applications of the Random Walk

  1994cited by this paper
• Inhomogeneous Systems with Unusual Critical Behaviour

  1993cited by this paper
• An Absorption Problem for Several Brownian motions

  1992cited by this paper
• Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk

  1992cited by this paper
• Directed polymer inside a parabola: Exact solution.

  1992cited by this paper
• Capture Problems For Coupled Random Walks

  1991cited by this paper
• Random walks, Brownian motion and interacting particle systems : a festschrift in honor of Frank Spitzer

  1991cited by this paper
• The reunions of three dissimilar vicious walkers

  1989cited by this paper
• Computer simulation methods for diffusion‐controlled reactions

  1988cited by this paper
• The reunions of three dissimilar vicious walkers

  1988cited by this paper
• Walks, walls, wetting, and melting

  1984cited by this paper
• Target annihilation by random walkers

  1984cited by this paper
• Kinetics of the 'scavenger' reaction

  1984cited by this paper
• Advanced Mathematical Methods for Scientists and Engineers

  1980cited by this paper
• Brownian first exit from and sojourn over one sided moving boundary and application

  1980cited by this paper
• The Asymptotic Theory of Extreme Order Statistics

  1979cited by this paper
• Advanced Mathematical Methods For Scientists And Engineers

  1979cited by this paper
• An introduction to probability theory

  1968cited by this paper
• Handbook of Mathematical Functions.

  1966cited by this paper
• Quantum Mechanics

  1961cited by this paper
• An Introduction to Probability Theory and Its Applications

  1959cited by this paper
• Conduction of Heat in Solids

  1947cited by this paper

• A first passage problem for a Poisson counting process with a linear moving boundary

  2026cites this paper
• Entropy production from density field theories for interacting particles systems

  2025cites this paper
• Recurrence in discrete-time quantum stochastic walks

  2025cites this paper
• A pursuit problem for squared Bessel processes

  2024cites this paper
• Analytical expressions for the first passage time distribution and hit distribution in two and three dimensions

  2024cites this paper
• Searching for a partially absorbing target by a run-and-tumble particle in a confined space.

  2023cites this paper
• Bernoulli trial under restarts: A comparative study of resetting transitions.

  2023cites this paper
• Non-Markovian and Collective Search Strategies

  2023cites this paper
• Dynamics at the edge for independent diffusing particles.

  2023cites this paper
• First-passage times of multiple diffusing particles with reversible target-binding kinetics

  2022cites this paper
• First-encounter time of two diffusing particles in two- and three-dimensional confinement.

  2022cites this paper
• Capture of a diffusing lamb by a diffusing lion when both return home.

  2022cites this paper
• Entropy production of nonreciprocal interactions

  2022cites this paper
• Statistical properties of sites visited by independent random walks

  2022cites this paper
• First passage time and information of a one-dimensional Brownian particle with stochastic resetting to random positions

  2022cites this paper
• Statistics of diffusive encounters with a small target: three complementary approaches

  2022cites this paper
• A hybrid method based on the orthogonal Bernoulli polynomials and radial basis functions for variable order fractional reaction-advection-diffusion equation

  2021cites this paper
• Diffusion in a fluid flow generated by a source at the apex of a wedge

  2021cites this paper
• Expected maximum of bridge random walks & Lévy flights

  2021cites this paper
• Capture of a diffusive prey by multiple predators in confined space.

  2020cites this paper
• Comparison of mechanisms of kinetochore capture with varying number of spindle microtubules

  2020cites this paper
• First-encounter time of two diffusing particles in confinement.

  2020cites this paper
• Redundancy, extreme statistics and geometrical optics of Brownian motion: Comment on "Redundancy principle and the role of extreme statistics in molecular and cellular biology" by Z. Schuss et al.

  2019cites this paper
• Redundancy principle and the role of extreme statistics in molecular and cellular biology.

  2019cites this paper
• Diffusive Search for Diffusing Targets with Fluctuating Diffusivity and Gating

  2019cites this paper
• How Receptor Surface Diffusion and Cell Rotation Increase Association Rates

  2019cites this paper
• Kinetochore capture by spindle microtubules: why fission yeast may prefer pivoting to search-and-capture

  2019cites this paper
• Geometrical optics of constrained Brownian motion: three short stories

  2019cites this paper
• Ordering statistics of four random walkers on a line.

  2018cites this paper
• Electromagnetic surface wave propagation in a metallic wire and the Lambert W function

  2018cites this paper
• Analyse diffusiver und intermittierender Suchstrategien mithilfe neuer Monte-Carlo-Algorithmen für allgemeine Reaktions-Diffusionsprobleme

  2017cites this paper
• Exploration properties of biased evanescent random walkers on a one-dimensional lattice

  2017cites this paper
• Anomalous dimension in a two-species reaction–diffusion system

  2017cites this paper
• Numerical analysis of homogeneous and inhomogeneous intermittent search strategies.

  2016cites this paper
• Constrained Probabilistic Search for a One-Dimensional Random Walker

  2016cites this paper
• A single predator charging a herd of prey: effects of self volume and predator–prey decision-making

  2016cites this paper
• Différentes propriétés de marches aléatoires avec contraintes géométriques et dynamiques

  2016cites this paper
• Diffusion with resetting in bounded domains

  2015cites this paper
• Run-and-tumble particles, telegrapher’s equation and absorption problems with partially reflecting boundaries

  2015cites this paper
• Capture rate and efficiency of an oscillating non-ideal trap interacting with a sea of random diffusing particles. A non-equilibrium Fokker–Planck picture

  2015cites this paper
• Survival probability of a Brownian motion in a planar wedge of arbitrary angle.

  2015cites this paper
• First-passage time of run-and-tumble particles

  2014cites this paper
• The role of target modeling in designing search strategies

  2014cites this paper
• First invader dynamics in diffusion-controlled absorption

  2014cites this paper
• Gradual diffusive capture: slow death by many mosquito bites

  2014cites this paper
• Cyclic pursuit problems in the two dimensional sphere

  2014cites this paper
• Searching for a one-dimensional random walker: Randomized strategy with energy budget

  2013cites this paper
• Evanescent continuous-time random walks.

  2013cites this paper
• Long-Term Search Through Energy Efficiency and Harvesting

  2013cites this paper
• First Passage Behavior of Multi-Dimensional Fractional Brownian Motion and Application to Reaction Phenomena

  2013cites this paper
• Persistence and first-passage properties in nonequilibrium systems

  2013cites this paper
• REVIEW ARTICLE Persistence and First-Passage Properties in Non-equilibrium Systems

  2013cites this paper
• First-passage characteristics of biased diffusion in a planar wedge.

  2013cites this paper
• Can a lamb reach a haven before being eaten by diffusing lions?

  2012cites this paper
• First passages for a search by a swarm of independent random searchers

  2011cites this paper
• A statistical model of aggregate fragmentation

  2011cites this paper
• Vicious walks with long-range interactions.

  2010cites this paper
• First passage in infinite paraboloidal domains

  2010cites this paper
• Maximum of N independent Brownian walkers till the first exit from the half-space

  2010cites this paper
• First-passage exponents of multiple random walks

  2010cites this paper
• Kinetics of first passage in a cone

  2010cites this paper
• Lifetime of a target in the presence of N independent walkers

  2010cites this paper
• First Passage Time Analysis of Animal Movement and Insights into the Functional Response

  2009cites this paper
• Survival of an evasive prey

  2009cites this paper
• 2 A ug 2 00 2 March 18 , 2008 Families of Vicious Walkers

  2008influential citation
• Mobile trap algorithm for zinc detection using protein sensors.

  2007cites this paper
• Diffusive capture processes for information search

  2007cites this paper
• Diffusive capture process on complex networks.

  2006cites this paper
• A framework for pursuit evasion games in Rn

  2005cites this paper
• Drowsy cheetah hunting antelopes: a diffusing predator seeking fleeing prey

  2004cites this paper
• Survival probability of a ballistic tracer particle in the presence of diffusing traps.

  2003cites this paper
• Some exact results for the trapping of subdiffusive particles in one dimension

  2003cites this paper
• Order statistics of Rosenstock's trapping problem in disordered media.

  2003cites this paper
• First-Passage Problems in Spatially Extended Systems

  2003cites this paper
• Persistence properties of a system of coagulating and annihilating random walkers.

  2003cites this paper
• Ordering of random walks: the leader and the laggard

  2002influential citation
• Perturbation theory for the one-dimensional trapping reaction

  2002cites this paper
• Go with the Winners: a General Monte Carlo Strategy

  2002cites this paper
• Survival probability and order statistics of diffusion on disordered media.

  2002cites this paper
• Families of vicious walkers

  2002influential citation
• Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps.

  2002cites this paper
• Multiparticle trapping problem in the half-line

  2001cites this paper
• 4 Dispersive kinetics

  2001cites this paper
• ‘Go with the Winners’ Simulations

  2000cites this paper