Title

Record-breaking statistics for random walks in the presence of measurement error and noise

Authors

Yaniv Edrey, Weizmann Institute of Science
Alexander Kostinski, Michigan Technological UniversityFollow
Satya N. Majumdar, Michigan Technological University
Brian Berkowitz, Weizmann Institute of Science

Document Type

Article

Publication Date

5-3-2013

Abstract

We examine distance record setting by a random walker in the presence of a measurement error δ and additive noise γ and show that the mean number of (upper) records up to n steps still grows universally as ⟨R_n⟩∼n^1/2 for large n for all jump densities, including Lévy distributions, and for all δ and γ. In contrast, the pace of record setting, measured by the amplitude of the n^1/2 growth, depends on δ and γ. In the absence of noise (γ=0), the amplitude S(δ) is evaluated explicitly for arbitrary jump distributions and it decreases monotonically with increasing δ whereas, in the case of perfect measurement (δ=0), the corresponding amplitude T(γ) increases with γ. The exact results for S(δ)offer a new perspective for characterizing instrumental precision by means of record counting. Our analytical results are supported by extensive numerical simulations.

Publisher's Statement

© 2013 American Physical Society. Publisher's version of record: https://doi.org/10.1103/PhysRevLett.110.180602

Publication Title

Physical Review Letters

Recommended Citation

Edrey, Y., Kostinski, A., Majumdar, S. N., & Berkowitz, B. (2013). Record-breaking statistics for random walks in the presence of measurement error and noise. Physical Review Letters, 110(18). http://doi.org/10.1103/PhysRevLett.110.180602
Retrieved from: https://digitalcommons.mtu.edu/physics-fp/186

Version

Publisher's PDF