2013/02/04 by Yaniv Edery, Alexander B. Kostinski, Satya N. Majumdar +1 · 26 citations
Mathematics · Physics and Astronomy · #Amplitude #Computer science #Jump #Mathematical analysis #Mathematics #Monotonic function #Noise (video) #Optics #Physics #Quantum mechanics #Random error #Random walk #Statistical Distribution Estimation and Applications #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #physics.data-an
paper · pdf · doi:10.1103/physrevlett.110.180602
published in Physical Review Letters 110(18), 180602 (American Physical Society)
arxiv created 2013/02/04 · openalex publication_date 2013/05/03 · arxiv updated 2013/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We examine distance record setting by a random walker in the presence of a measurement error \ensuremathδ and additive noise \ensuremathγ and show that the mean number of (upper) records up to n steps still grows universally as ⟨Rn⟩\ensuremath∼n1/2 for large n for all jump densities, including L'evy distributions, and for all \ensuremathδ and \ensuremathγ. In contrast, the pace of record setting, measured by the amplitude of the n1/2 growth, depends on \ensuremathδ and \ensuremathγ. In the absence of noise (\ensuremathγ=0), the amplitude S(\ensuremathδ) is evaluated explicitly for arbitrary jump distributions and it decreases monotonically with increasing \ensuremathδ whereas, in the case of perfect measurement (\ensuremathδ=0), the corresponding amplitude T(\ensuremathγ) increases with \ensuremathγ. The exact results for S(\ensuremathδ) offer a new perspective for characterizing instrumental precision by means of record counting. Our analytical results are supported by extensive numerical simulations.