Fig. 3: Universal record age distributions for non-Markovian RWs: theoretical predictions (lines) vs experimental RW realisations and real time observations (symbols).

a–h Distribution of the increment x_t = X_t+T − X_T at different times t normalised by \({t}^{1/{d}_{{{{{{{{\rm{w}}}}}}}}}}\) for: (a) river discharge (t = 10, 20, and 40), (b) volcanic soil temperature (t = 5, 10, and 20), (c) motion of microspheres in a gel (t = 2, 4, and 8), (d) motion of vacuoles inside an amoeba (t = 10, 20, and 40), (e) motion of telomeres (t = 20, 40, and 80), (f) DNA RW (t = 20, 40, and 80), (g) cumulative air temperature (t = 5, 10, and 20), and (h) Ethernet cumulative requests (t = 500, 1000, and 2000). Increasing values of times are represented successively by blue circles, orange stars and green squares. a\({}^{{\prime} }\)–d\({}^{{\prime} }\) Statistics of the time to first reach the initial value in the sub interval (blue stars) and the statistics of the records (regardless of the number n of records, orange circles) for (a\({}^{{\prime} }\)) river discharge, (b\({}^{{\prime} }\)) volcanic soil temperature, (c\({}^{{\prime} }\)) motion of microspheres in a gel, and (d\({}^{{\prime} }\)) motion of vacuoles inside an amoeba. The black dashed line represents the algebraic decay \({\tau }^{-1+1/{d}_{{{{{{{{\rm{w}}}}}}}}}}\) while the red dashed line stands for the algebraic decay \({\tau }^{-1/{d}_{{{{{{{{\rm{w}}}}}}}}}}\). (e\({}^{{\prime} }\)–h\({}^{{\prime} }\)) Rescaled tail distribution of record ages τ_n for different values of the number of records n for (e\({}^{{\prime} }\)) motion of telomeres (n = 1, 3, and 6), (f\({}^{{\prime} }\)) DNA RW (n = 1, 2, and 4), (g\({}^{{\prime} }\)) cumulative air temperatures (n = 1, 2, and 3), and (h\({}^{{\prime} }\)) Ethernet cumulative requests (n = 1, 5, and 25). Increasing values of n are represented successively by blue circles, orange stars, and green squares. The lines represent the algebraic decays as for (a\({}^{{\prime} }\)–d\({}^{{\prime} }\)).