Year: 2016
Type: article
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 ${x(t)},0\ensuremath{\le}t\ensuremath{\le}\ensuremath{\tau}$, with boundary conditions $x(0)=N$ and $x(\ensuremath{\tau})$ = 1. This model is shown to be exactly solvable: ${\mathcal{P}}_{N}(\ensuremath{\tau})$, the probability that the process survives for time $\ensuremath{\tau}$ 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: $\ensuremath{\langle}\ensuremath{\tau}\ensuremath{\rangle}\ensuremath{\sim}lnN$ and ${\ensuremath{\sigma}}_{\ensuremath{\tau}}^{2}\ensuremath{\sim}lnN$. Correspondence can be made between survival-time statistics in the SSR process and record statistics of independent and identically distributed random variables.
Source: Physical review. E
Author: Avinash Chand Yadav
Institution: Central University of Haryana
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2289078448