title: Survival-time statistics for sample space reducing stochastic processes.
abstract: Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic process that results in a random sequence of strictly decreasing integers {x(t)},0≤t≤τ, with boundary conditions x(0)=N and x(τ) = 1. This model is shown to be exactly solvable: P_{N}(τ), the probability that the process survives for time τ is analytically evaluated. In the limit of large N, the asymptotic form of this probability distribution is Gaussian, with mean and variance both varying logarithmically with system size: 〈τ〉∼lnN and σ_{τ}^{2}∼lnN. Correspondence can be made between survival-time statistics in the SSR process and record statistics of independent and identically distributed random variables.
authors.affiliation: School of Physical & Mathematical Sciences, Central University of Haryana, Mahendergarh 123 029, India.
authors.forename: Avinash Chand
authors.initials: AC
authors.lastname: Yadav