Brownian motion in dire straits

D. Holcman, Z. Schuss

Research output: Contribution to journalArticlepeer-review


The passage of Brownian motion through a bottleneck in a bounded domain is a rare event, and as the bottleneck radius shrinks to zero the mean time for such passage increases indefinitely. Its calculation reveals the effect of geometry and smoothness on the flux through the bottleneck. We find new behavior of the narrow escape time through bottlenecks in planar and spatial domains and on a surface. Some applications in cellular biology and neurobiology are discussed.

Original languageEnglish
Pages (from-to)1204-1231
Number of pages28
JournalMultiscale Modeling and Simulation
Issue number4
StatePublished - 2012


  • Asymptotic analysis
  • Boundary layer
  • Brownian motion
  • Conformal mapping
  • Diffusion
  • First eigenvalue
  • Laplace equation
  • Mean first passage time
  • Mixed Dirichlet-Neumann boundary value problem
  • Narrow escape
  • Small hole
  • Stochastic processes


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