Record events in growing populations: universality, correlation, and aging.
This paper studies the occurrence of record events in score populations which grow stochastically in time. In Rényi's basic record model, a population of independent and identically distributed (i.i.d.) random scores grows deterministically--a single new score being added at each time step. Rényi's record theorem asserts that the resulting record events are independent, and that their occurrence probabilities decrease harmonically in time. Moreover, Rényi's result is universal--being independent of the distribution of the i.i.d. random scores. This paper considers an arbitrary stochastic growth of the score population--allowing the number of the i.i.d. random scores added at each time step to follow arbitrary stochastic dynamics. Exploring the stochastic growth model we: (i) establish a general analog of Rényi's record theorem; (ii) show that universality with respect to the distribution of the i.i.d. random scores is maintained; (iii) compute the distribution of the waiting times for record events; (iv) analyze the dependencies/independencies of the record events; and (v) analyze the aging/stationarity of the record events.
Eliazar
Iddo
I
Department of Technology Management, Holon Institute of Technology, PO Box 305, Holon 58102, Israel. eliazar@post.tau.ac.il
Klafter
Joseph
J
D017677:Age Distribution; D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D008954:Models, Biological; D015233:Models, Statistical; D011158:Population Growth; D013223:Statistics as Topic