Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains

Abstract

How long does a diffusing molecule spend in a close vicinity of a confining boundary or a catalytic surface? This quantity is determined by the boundary local time, which plays thus a crucial role in the description of various surface-mediated phenomena such as heterogeneous catalysis, permeation through semi-permeable membranes, or surface relaxation in nuclear magnetic resonance. In this paper, we obtain the probability distribution of the boundary local time in terms of the spectral properties of the Dirichlet-to-Neumann operator. We investigate the short-time and long-time asymptotic behaviors of this random variable for both bounded and unbounded domains. This analysis provides complementary insights onto the dynamics of diffusing molecules near partially reactive boundaries.

References in corpus (16)

• Geometry-controlled kinetics
• Geometrical structure of Laplacian eigenfunctions
• Optimal reaction time for surface-mediated diffusion
• Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions
• Mortality, Redundancy, and Diversity in Stochastic Search
• Kinetics of stochastically-gated diffusion-limited reactions and geometry of random walk trajectories
• Averaged residence times of stochastic motions in bounded domains
• Exploration and Trapping of Mortal Random Walkers
• The escape problem for mortal walkers
• Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces
• Explicit Construction of the Brownian Self-Transport Operator
• Partially Reflected Brownian Motion: A Stochastic Approach to Transport Phenomena
• On the Robin problem in fractal domains
• First exit times and residence times for discrete random walks on finite lattices
• Narrow-escape-time problem: the imperfect trapping case
• Residence Time Near an Absorbing Set

Cited by in corpus (27)

• Paradigm shift in diffusion-mediated surface phenomena
• Surface Hopping Propagator: An Alternative Approach to Diffusion-Influenced Reactions
• Diffusion toward non-overlapping partially reactive spherical traps: fresh insights onto classic problems
• Statistics of boundary encounters by a particle diffusing outside a compact planar domain
• Large deviations of currents in diffusions with reflective boundaries
• Joint distribution of multiple boundary local times and related first-passage time problems with multiple targets
• Depletion of Resources by a Population of Diffusing Species
• Statistics of diffusive encounters with a small target: Three complementary approaches
• Encounter-based approach to diffusion with resetting
• Distribution of first-reaction times with target regions on boundaries of shell-like domains
• An encounter-based approach to the escape problem
• First-encounter time of two diffusing particles in two- and three-dimensional confinement
• Spectral properties of the Dirichlet-to-Neumann operator for spheroids
• Low energy scattering asymptotics for planar obstacles
• Local time of an Ornstein-Uhlenbeck particle
• Exploring run-and-tumble movement in confined settings through simulation
• Contact statistics in populations of noninteracting random walkers in two dimensions
• Inter-particle ratchet effect determines global current of heterogeneous particles diffusing in confinement
• Subdiffusion in the Presence of Reactive Boundaries: A Generalized Feynman-Kac Approach
• Escape-from-a-layer approach for simulating the boundary local time in Euclidean domains
• The Steklov problem for exterior domains: asymptotic behavior and applications
• Concentration of Empirical First-Passage Times
• Adsorption and permeation events in molecular diffusion
• Single file dynamics of tethered random walkers
• Encounter-based approach to target search problems: a review
• From Reflecting Brownian Motion to Reflected Stochastic Differential Equations: A Systematic Survey and Complementary Study
• An encounter-based approach for restricted diffusion with a gradient drift