First-passage-time exponent for higher-order random walks: Using Lévy flights

Jennifer M Schwarz, Ron Maimon

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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 (Formula presented) We discuss the implications of this estimation scheme for the (Formula presented) integral of a random walk. For completeness, we also address the (Formula presented) 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.

Original languageEnglish (US)
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume64
Issue number1
DOIs
StatePublished - Jan 1 2001
Externally publishedYes

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First Passage Time
random walk
Random walk
Exponent
flight
exponents
Higher Order
derivation
Reparametrization
Random Potential
Nonlinear Process
Langevin Equation
stochastic processes
completeness
Stochastic Processes
Completeness
Heuristics
Demonstrate

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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abstract = "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 (Formula presented) We discuss the implications of this estimation scheme for the (Formula presented) integral of a random walk. For completeness, we also address the (Formula presented) 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.",
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