Extremes and Records

Abstract

These are lecture notes from a course offered at the Bangalore School on Statistical Physics - X, during 17-28 June 2019, [ https://www.icts.res.in/program/bssp2019 ] at International centre of theoretical physics (ICTS), Bangalore. These pedagogical lectures are at the introductory level, intended mainly for master/Ph.D. students or researchers from outside the field. In these lectures, we discuss about the limit laws for the sample mean and the maximum of a set of independent and identically distributed (i.i.d.) random variables as well as random walks / Brownian motion. The density of near-extreme events is also discussed. Finally, we discuss the statistics of records for an i.i.d. random sequence as well as random walks in discrete and continuous time. Some exercises are provided for the students to work out. The video recording of the lectures are available at https://www.icts.res.in/program/bssp2019/talks