2001/03/09 by J. M. Schwarz, Ron Maimon · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Stochastic processes and statistical mechanics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.64.016120
4 figures, submitted to PRE
arxiv created 2001/03/09 · openalex publication_date 2001/06/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a heuristic derivation of the first-passage-time exponent for the integral of a random walk [Y. G. Sinai, Theor. Math. Phys. 90, 219 (1992)]. Building on this derivation, we construct an estimation scheme to understand the first-passage-time exponent for the integral of the integral of a random walk, which is numerically observed to be 0.220+/-0.001. We discuss the implications of this estimation scheme for the nth integral of a random walk. For completeness, we also address the n=infinity case. Finally, we explore an application of these processes to an extended, elastic object being pulled through a random potential by a uniform applied force. In so doing, we demonstrate a time reparametrization freedom in the Langevin equation that maps nonlinear stochastic processes into linear ones.