2013/05/03 by Grégory Schehr, Gregory Schehr, Satya N. Majumdar +2
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Data Analysis #Diffusion and Search Dynamics #FOS: Economics and business #FOS: Mathematics #FOS: Physical sciences #Probability (math.PR) #Quantum chaos and dynamical systems #Statistical Finance (q-fin.ST) #Statistical Mechanics (cond-mat.stat-mech) #Statistics and Probability (physics.data-an) #cond-mat.stat-mech #math.PR #physics.data-an #q-fin.ST
paper · pdf · doi:10.48550/arxiv.1305.0639
25 pages, 2 figures. To appear in the special volume "First-Passage Phenomena and Their Applications", Eds. R. Metzler, G. Oshanin, S. Redner. World Scientific (2013)
arxiv created 2013/05/03 · openalex publication_date 2013/05/03 · arxiv updated 2013/05/06 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
While records and order statistics of independent and identically distributed (i.i.d.) random variables X1, ..., XN are fully understood, much less is known for strongly correlated random variables, which is often the situation encountered in statistical physics. Recently, it was shown, in a series of works, that one-dimensional random walk (RW) is an interesting laboratory where the influence of strong correlations on records and order statistics can be studied in detail. We review here recent exact results which have been obtained for these questions about RW, using techniques borrowed from the study of first-passage problems. We also present a brief review of the well known (and not so well known) results for records and order statistics of i.i.d. variables.