{
  "id": "1801.05446",
  "version": "v1",
  "published": "2018-01-16T19:00:52.000Z",
  "updated": "2018-01-16T19:00:52.000Z",
  "title": "The Stretch to Stray on Time: Resonant Length of Random Walks in a Transien",
  "authors": [
    "Martin Falcke",
    "V. Nicolai Friedhoff"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "q-bio.MN",
    "q-fin.MF"
  ],
  "abstract": "First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average first-passage time, or control might be applied to reduce noise. We investigate moments of the first-passage time distribution under a transient describing relaxation of environmental conditions. We solve the Laplace-transformed (generalized) master equation analytically using a novel method that is applicable to general state schemes. The first-passage time from one end to the other of a linear chain of states is our application for the solutions. The dependence of its average on the relaxation rate obeys a power law for slow transients. The exponent $\\nu$ depends on the chain length $N$ like $\\nu=-N/(N+1)$ to leading order. Slow transients substantially reduce the noise of first-passage times expressed as the coefficient of variation (CV), even if the average first-passage time is much longer than the transient. The CV has a pronounced minimum for some lengths, which we call resonant lengths. These results also suggest a simple and efficient noise control strategy, and are closely related to the timing of repetitive excitations, coherence resonance and information transmission by noisy excitable systems. A resonant number of steps from the inhibited state to the excitation threshold and slow recovery from negative feedback provide optimal timing noise reduction and information transmission.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-16T19:00:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random walks",
      "resonant length",
      "average first-passage time",
      "efficient noise control strategy",
      "environmental conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}