Statistical error in simulations of Poisson processes: Example of diffusion in solids

Johan O. Nilsson, Mikael Leetmaa, Olga Yu. Vekilova, Sergei I. Simak, Natalia V. Skorodumova
2016 Physical review B  
Simulations of diffusion in solids often produce poor statistics of diffusion events. We present an analytical expression for the statistical error in ion conductivity obtained in such simulations. The error expression is not restricted to any computational method in particular, but valid in the context of simulation of Poisson processes in general. This analytical error expression is verified numerically for the case of Gd-doped ceria by running a large number of kinetic Monte Carlo
more » ... te Carlo calculations. NILSSON, LEETMAA, VEKILOVA, SIMAK, AND SKORODUMOVA PHYSICAL REVIEW B 94, 085206 (2016) TABLE I. Statistical error for simulations of different length n. num J is the numerical relative error and analyt J is the analytical relative error defined in this section. n num J [%] analyt J
doi:10.1103/physrevb.94.085206 fatcat:q7c4rlefk5e25gurjayerguc5i