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 ⟨Rn⟩∼n1/2 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 n1/2 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

Publication Title

Physical Review Letters

Version

Publisher's PDF

Included in

Physics Commons

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