2002/12/17 by L Turban, L. Turban
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/36/14/305
published as J. Phys. A 36 (2003) 3995--4005 · 12 pages, 2 figures
arxiv created 2002/12/17 · openalex publication_date 2003/03/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The crossing probability in the time direction, π t , is defined for an off-equilibrium reaction–diffusion system as the probability that the system of size L is still active at time t , in the finite-size scaling limit. Exact results are obtained for the diffusion-limited coalescence problem in 1 + 1 dimensions with periodic and free boundary conditions using empty interval methods. π t is a scale-invariant universal function of an effective aspect ratio, L 2 / Dt , which is the natural scaling variable for this strongly anisotropic system.