On the weak limit law of the maximal uniform k-spacing

2015/08/05 by Aleksandar Mijatović, Mijatović, Aleksandar, Vladislav Vysotsky +1
Decision Sciences · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 60F05 #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #secondary 60G70

paper · pdf · doi:10.48550/arxiv.1508.00944

openalex publication_date 2015/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives a simple proof of a limit theorem for the lenght of the largest interval straddling a fixed number of i.i.d. points uniformly disributed on a unit interval. The key step in our argument is a classical theorem of Watson (1954) on the maxima of m-dependent stationary stochastic sequences.

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